Financial and Actuarial Mathematics Seminars

Wednesday 27th May 2020  From the LokkaZervos alternative to Riemann Surfaces
Speaker : Professor Florin Avram (University of Pau)
14:00 Via Zoom
Abstract : We discuss the following question: For risk models with dividends and possible capital injections with proportional costs, when should we use capital injections rather than declaring bankruptcy? The talk is based on several joint papers (mostly future) with Dan Goreac, JeanFrancois Renaud, Bo Li, and Pingping Jiang.

Wednesday 20th May 2020  Finitetime Ruin Probability for Markovian Skipfree Risk Processes
Speaker : Professor Pierre Patie (University of Liverpool)
14:00 Via Zoom
Abstract : In this talk, we study the ruin problem for a risk process whose dynamics is given as an upward skipfree continuoustime Markov process. It means that the surplus process has upward jumps of unit size, yet it can have downward transition of arbitrary magnitude. By resorting to the theory of Martin boundary, we start by providing a representation of the green function of this Markov process in terms of some fundamental excessive functions, extending the seminal work of Feller for diffusions. We proceed by deriving an expression of the Laplace transform of the time of ruin that may occur by a jump. We end the talk by detailing some examples that illustrate our methodology.

11th March 2020  Minimizing the expected time in Drawdown
Speaker: Leonie Brinker
13:00 Math 104
Abstract: We consider a diffusion approximation to an insurance risk model. In this context the drawdown of the process is defined as the absolute distance from the running maximum. The insurer is allowed to buy proportional reinsurance to minimize the expected discounted time the drawdown process exceeds some critical value d.Both insurer and reinsurer charge premiums which are calculated via the expected value principle. We obtain explicit results for the value function, the optimal strategy and their dependence on the safety loading of the reinsurance premium.
The optimal strategy resulting from the minimization of drawdowns is solely influenced by negative deviation from the running maximum. As an extension to the model we introduce an incentive to grow. In particular, we assume that the insurer pays out dividends following a barrier strategy. We consider the postdividend process under proportional reinsurance and maximize the value of the expected discounted dividends minus a penalization for time spent in drawdown. 
Wednesday 19th February 2020  Matrix distributions, MittagLeffler functions and the modeling of heavytailed risks
Speaker: Professor Hansjoerg Albrecher, University of Lausanne
13:00 Mount Pleasant 126 Room 116
Abstract: In this talk we discuss the extension of the construction principle of phasetype (PH) distributions to allow for inhomogeneous transition rates and show that this naturally leads to direct probabilistic descriptions of certain transformations of PH distributions. In particular, the resulting matrix distributions enable to carry over fitting properties of PH distributions to distributions with heavy tails, providing a general modelling framework for heavytail phenomena. We also discuss related randomized versions involving MittagLeffler distributions and illustrate the versatility and parsimony of the proposed approach for the modelling of realworld insurance data.

Wednesday 12th February 2020  Stochastic inversions and Kelvin Transform
Speaker: Larbi Alili, University of Warwick
14:00 MATH106
Abstract: I will show that a space time inversion of a strong Markov process X implies the existence of a Kelvin transform of harmonic functions. We determine new classes of processes having space inversion properties amongst transient processes satisfying the time inversion property. For these processes, some explicit inversions which are often not the spherical ones and excessive functions are given explicitly. We treat in details some examples.

Tuesday 5th February 2020  Optimal Reinsurance and Investment in a Diffusion Model
Speaker: Hanspeter Schmidli, University of Cologne, Germany.
14:00 MATH106
Abstract: We consider a diffusion approximation to an insurance risk model where an external driver models a stochastic environment. The insurer can buy reinsurance. Moreover, it is possible to invest in a financial market that depends on the insurance market. The financial market is also driven by the environmental process. Our goal is to maximise terminal expected utility. In particular, we consider the case of SAHARA utility functions. In the case of proportional and excessofloss reinsurance, we obtain explicit results. (Joint work with Matteo Brachetta, Pescara).

Tuesday 28th January 2020  A ruin model with a resampled environment
Speaker: Guusje Delsing, University of Amsterdam
14:00: 126 Mount Pleasant Room 116
Abstract: We consider a CramérLundberg risk setting, where the components of the underlying model change over time. These components could be thought of as the claim arrival rate, the claimsize distribution, and the premium rate, but we allow the more general setting of the cumulative claim process being modelled as a spectrally positive Lévy process. We provide an intuitively appealing mechanism to create such parameter uncertainty: at Poisson epochs we resample the model components from a finite number of $d$ settings. It results in a setup that is particularly suited to describe situations in which the risk reserve dynamics are affected by external processes (such as the state of the economy, political developments, weather or climate conditions, and policy regulations).
We extend the classical CramérLundberg approximation (asymptotically characterizing the alltime ruin probability in a lighttailed setting) to this more general setup. In addition, for the situation that the driving Lévy processes are sums of Brownian motions and compound Poisson processes, we find an explicit uniform bound on the ruin probability, which can be viewed as an extension of Lundberg's inequality; importantly, here it is not required that the Lévy processes be spectrally onesided. In passing we propose an importancesampling algorithm facilitating efficient estimation, and prove it has bounded relative error. In a series of numerical experiments we assess the accuracy of the asymptotics and bounds, and illustrate that neglecting the resampling can lead to substantial underestimation of the risk.

15th January 2020  Statistical tools to manage longevity risk
Speaker: Ana Debron Universitat Politècnica de València (Spain)
13:00 Mount Pleasant 126, Room 209
Abstract :The statistical methodology that this article proposes was applied with the aim of establishing an operating procedure which permits to detect associations between countries with similar mortality, in particular the European Union countries. Once confirmed the significant associations, we implemented a spatial model for panel data.

Wednesday 11th December 2019  Dependence uncertainty bounds for the energy score
Speaker: Alfred Müller (University of Siegen)
14:00 MATH106
Abstract: Authors: Alfred Müller, Carole Bernard
There is an increasing interest in recent years in methods for assessing the quality of probabilistic forecasts by so called scoring rules. For forecasting general multivariate distributions, however, there are only a very few scoring rules that are considered in the literature. In their fundamental paper, Gneiting and Raftery (2007) considered the so called energy score as an example of a scoring rule that is strictly proper for arbitrary multivariate distributions. Pinson and Tastu (2013) started a debate on the discrimination ability of this scoring rule with respect to the dependence structure.
In this paper we want to contribute to this discussion by deriving dependence uncertainty bounds for the energy score and the related multivariate Gini mean difference. This means that we derive bounds for the score under the assumption that we only know the marginals of the distributions, but do not know anything about the dependence structure, i.e. the copula. Using methods from stochastic orderings we will derive some analytical bounds that are sharp in some cases. In other cases we will derive interesting numerical bounds by using a variant of a swapping algorithm. It turns out that some of these bounds are attained for some nonstandard copulas that are of interest in their own right.
Keywords: multivariate probabilistic forecasts, energy score, dependence uncertainty, stochastic orderings 
Wednesday 4th December 2019  Pricing and hedging with rough volatility
Speaker: Dr. David R. Banos (University of Oslo)
14:00 MATH106
Abstract: Stochastic volatility models are not complete, as one is considering more than one source of noise. Nevertheless, in some cases, one can trade futures on the socalled forward volaility/variance. This is e.g. the case for the S&P 500 index and the VIX index where the latter is a measure of the stock market's expectation of the volatility implied by S&P 500. In such case, one can replicate any squareintegrable derivative using classical technices, e.g. PDEtechniques.
There has been some research providing empirical evidence that volaility actually is rough in the sense of fractional Brownian motion. In this talk we consider a general framework where the stochastic volatility is of Volterra type (e.g. it can be driven fractional Brownian motion), in such case, the forward variance is no longer Markov and the PDEtechnique fails. We use the socalled benchmark approach to price derivatives under the realworl measure P, and not the classical riskneutral measure Q and use Malliavin calculus to find hedging portfolios.

Wednesday 13th November 2019  Epiphanies in Pension Design and Valuation
Speaker: Professor Mogens Steffensen, University of Copenhagen
14:00 MATH106
Abstract: We discuss, on a principle rather than a technical ground, three instances where things are perhaps not the way you thought they were  with potential impact, theoretically or practically. a) In lifecycle portfolio choice, does one really need to take realized capital gains into account, or are agebased investment rules doing the job? b) In timeconsistent meanvariance portfolio optimization, is normalization of the variance by current wealth really the 'right' thing to do, or is there a 'better' normalization? c) In multistate models frequently used in life insurance and credit risk, does there exist such a thing as a set of forward transition rates?

Wednesday 30th October 2019  Valuation of Insurance Liabilities: Merging Market  and ModelConsistency
Speaker: Prof. Jan Dhaene, KU Leuven, Belgium
14:00 MATH106
Abstract: We investigate the valuation of liabilities related to an insurance policy or portfolio in a single period framework. We define a fair valuation as a valuation which is both marketconsistent (marktomarket for any hedgeable part of a claim) and modelconsistent (marktomodel for any claim that is independent of financial market evolutions). We introduce the class of hedgebased valuations, where in a first step of the valuation process, a ‘best hedge’ for the liability is set up, based on the traded assets in the market, while in a second step, the remaining part of the claim is valuated via an actuarial model. We also introduce the class of twostep valuations, the elements of which are very closely related to the twostep valuations which were introduced in Pelsser and Stadje (2014). We show that the classes of fair, hedgebased and twostep valuations are identical.

Wednesday 23rd October 2019  Peano curves, trees, and spheres
Speaker: Dr Daniel Meyer (University of Liverpool)
14:00 MATH106
Abstract: In this talk I will explore connections between three different fields, namely random geometry, complex dynamics, and hyperbolic geometry. The first object is the "Brownian map'', introduced by Le Gall. This is a random metric space which is a topological 2sphere. It can be thought of as a 2dimensional analog of Brownian motion. The second construction, from complex dynamics, is the "mating of polynomials'' introduced by Douady and Hubbard. Here the Julia sets of two polynomials are glued together, which often results in a rational map (i.e., a holomorphic map on the Riemann sphere). The third construction, from hyperbolic geometry, are "manifolds that fiber over the circle'' and closely related "group invariant Peano curves'' by Cannon and Thurston. In each of these constructions certain trees (random, or coming from a dynamical system) are glued together, resulting in a sphere with a Peano (i.e., space filling) curve. This is an instance of "Sullivan's dictionary''. I will be giving an overview of these 3 objects/constructions, without going into details/technicalities.

Wednesday 1st May 2019  On a Missing Characteristic in the Theory of Semimartingales
Speaker: Alexander Schnurr (Head of Math Department in the University of Siegen)
Venue: MATH105 14:00
Abstract: We extend the class of semimartingales in a natural way. This allows us to incorporate processes having paths that leave the state space. By carefully distinguishing between two killing states, we are able to introduce a fourth semimartingale characteristic which generalizes the fourth part of the Levy quadruple. Since three characteristics have become canonical over the years, we motivate the fourth characteristic also by considering Feller processes. Analyzing their generator, we find a natural fourth component which does not have an analogue in the theory of semimartingales yet. Our fourth characteristic completes a classical picture and allows to incorporate ane process (with killing) and nonconservative solutions to martingale problems in the semimartingale framework. Using the probabilistic symbol, we analyze the close relationship between the generators of certain Markov processes with killing and their (now four) semimartingale characteristics.

Wednesday 27th March 2019  Medium Data and SocioEconomic Mortality
Speaker: Prof Andrew Cairns (Heriot Watt University)
14:00 MATH105
Abstract: In this talk we will investigate what types of information about where you live affects mortality and life expectancy.
Data:
 ONS population and deaths data at the level of small geographical areas (LSOA's)
 socioeconomic covariates for each LSOA
 geographical covariates for each LSOA.
We will discuss first which combination of covariates have the strongest predictive power. Second we will investigate how much regional variation there is in our resulting models: is region a genuinely significant factor in the level of mortality or is observed regional variation simply reflecting differences in the socioeconomic makeup of local populations.
The use of advanced statistical methods will allow us to investigate how much variation there is across England in mortality rates and life expectancy. We can then use that to inform mortality assumption setting in pension scheme valuations.

Wednesday 20th March 2019  Insurance risk pooling, loss coverage and social welfare: When is adverse selection not adverse?
Speaker: Pradip Tapadar (University of Kent)
14:00 MATH105
Abstract: Restrictions on insurance risk classification may induce adverse selection, which is usually perceived as a bad outcome, both for insurers and for society. We suggest a counterargument to this perception in circumstances where modest levels of adverse selection lead to an increase in `loss coverage’, defined as expected losses compensated by insurance for the whole population. This happens if the shift in coverage towards higher risks under adverse selection more than offsets the fall in number of individuals insured. We also reconcile the concept of loss coverage to a utilitarian concept of social welfare commonly found in economic literature. For isoelastic insurance demand, ranking risk classification schemes by (observable) loss coverage always gives the same ordering as ranking by (unobservable) social welfare.

Wednesday 6th March 2019  Yield Curves, Measure Transformation, and Applications in ChanceRisk Classification of German Pension Products
Speaker: Ralf Korn (TU Kaiserslautern)
14:00PM Room: MATH105
Abstract: Yield curves display the equivalent fixed yield of zero bonds for different maturities when they are bought and hold until maturity. Thus, the yield curve describes the actual fixed income opportunities prefectly.
For reasons of e.g. product development or chancerisk classification of pension products simulation for up to 40 years is performed. We therefore examine the different forms of yield curves generated by classical affine models and the dynamic evolution of their distribution.
Finally, we present a measure transformation approach that can be used to conserve empirical distribution properties of yield curves with evolving time.

Wednesday 20th February 2019  Cascade Sensitivity Measures
Speaker: Silvana Pesenti (Faculty of Actuarial Science and Insurance, Cass Business School, City, University of London)
14:00PM Room: MATH105
Abstract: Sensitivity measures quantify the extent to which the distribution of a model output is affected by small changes (stresses) in an individual random input factor. For input factors that are dependent, a stress on one input should also precipitate stresses in other input factors. We introduce a novel sensitivity measure, termed cascade sensitivity, which captures the direct impact of the stressed input factor on the output, as well as indirect effects via other input factors that are dependent on the one being stressed. In this way, the dependence between inputs is explicitly taken into account. Representations of the cascade sensitivity measure, which can be calculated from one single Monte Carlo sample, are provided for two types of stress: a) a perturbation of the distribution of an input factor, such that the stressed input follows a mixture distribution, and b) an additive random shock applied to the input factor. These representations do not require simulations under different model specifications or the explicit study of the properties of the model's aggregation function, making the proposed method attractive for practical applications, as we illustrate through numerical examples.

Thursday 14th February 2019  LeedsLiverpool joint workshop on Optimization, Uncertainty, Actuarial and Financial Mathematics
Venue: 11:0013:00 502LT1 and 14:0017:00 CHEMGOS
Speakers:
11:30  Jan Palczewski (University of Leeds)  Value of Stopping Games with Asymmetric Information12:00  Apostolos Papaioannou (University of Liverpool) and Lewis Ramsden (University of Hertfordshire)  On Risk Models with Dependent Delayed Capital Injections
14:00  Katia Colaneri (University of Leeds)  Optimal Converge Trading with Unobservable Pricing Errors
14:30  Carmen Boado Penas (University of Liverpool)  Automatic Balancing Mechanisms for Mixed Pension Systems under Different Investment Strategies
15:30  Tiziano De Angelis (University of Leeds)  Optimal Dividends with Partial Information and Stopping of a Degenerate Reflecting Diffusion
16:00  Paul Eisenberg (University of Liverpool)  Occupation Estimates
Click here for full details and abstracts

Wednesday 6th February 2019  On the WienerHopf Factorization
Speaker: Prof Takis Konstantopoulos (University of Liverpool)
13:00 MATH211
Abstract: This is a talk on a classical topic seeing from a probabilist's viewpoint. Traditionally, the WienerHopf method is a tool in applied mathematics used, for example, to solve PDEs on the plane with mixed boundary conditions. Roughly speaking, it splits a complex function into a suitable product. For example, the design of a Wiener filter (linear estimation in stationary environment) is precisely a WienerHopf factorization. Our interest is in the derivation of the law of the overall supremum of a random walk. The law can be characterized by its Laplace transform, a complex analytic function and the WienerHopf factorization of it yields some magic that can be explained using Probability Theory. The ideas go back to Rogozin, Kolmogorov, et al, and are sometimes referred to as path decomposition methods. They boil down to a splitting of the path of a random walk into independent excursions, a simple application of the trivial "découpage de Lévy" identity, and a careful application of the two fundamental symmetries of a random walk:timereversal and spacereflection. Our goal is to show but one instance where Probability and Analysis meet and where Probability can be used to explain purely analytical concepts and derive purely analytical identities.

Wednesday 12th December 2018  Stochastic systems under parameter uncertainty
Speaker: Michel Mandjes (University of Amsterdam)
15:00PM Room: MATH105
Abstract: Poisson processes are frequently used, e.g. to model the customer arrival process in service systems, or the claim arrival process in insurance models. In various situations, however, the fluctuations in the arrival rate are so severe that the Poisson assumption ceases to hold. In a commonly followed approach to remedy this, the deterministic parameter λ is replaced by a stochastic process Λ(t). In this way the arrival process becomes overdispersed.
The first part of this talk considers the case that the Poisson rate is sampled periodically, with a focus on an infiniteserver queue fed by the resulting overdispersed arrival process. After having presented a functional central limit theorem, we concentrate on tail probabilities under a particular scaling of the arrival process and the sampling frequency. We derive logarithmic tail asymptotics, and in specific cases even exact tail asymptotics.
In the second part of the talk we embed our overdispersion setting in a more general framework. The probability of interest is expressed in terms of the composition of two Lévy processes, which can alternatively be seen as a Lévy process with random time change. For this twotimescale model we present exact tail asymptotics. The proof relies on an adaptation of classical techniques developed by Bahadur and Rao, in combination with delicate Edgeworth expansion arguments. The resulting asymptotics have a remarkable form, with finitely many sublinear terms in the exponent.
I finish my presentation by sketching a proof of convergence of the resampled M/M/1 queue (in heavy traffic) to reflected Brownian motion. (Joint work with Mariska Heemskerk, Julia Kuhn and Onno Boxma)

Tuesday 27th November 2018  Minimum reversion in multivariate time series (with an application to human mortality data)
Speaker: Torsten Kleinov (HeriotWatt University)
14:00PM Room: 126MP110
Abstract: We propose a new multivariate time series model in which we assume that each individual component has a tendency to revert to the minimum of all components. Such a specification is useful to describe phenomena where the behaviour of the best performing member in a population which is subjected to random noise is mimicked by other members. We show that the proposed dynamics generate cointegrated processes, characterize the model’s asymptotic properties for the case of two populations and show the stabilizing effect on long term dynamics in simulation studies. An empirical study involving human survival data in different countries provides an example which confirms the occurrence of the phenomenon of reversion to the minimum in real data.

Wednesday 21st November 2018  Distributionconstrained optimal stopping problems
Speaker: Christiane Elgert (TU Wien  Technical University of Vienna)
14:00PM Room: MATH105
Abstract: We deal with financial and actuarial products whose payouts are driven by stochastic processes. The time point of the payouts is modelled by an stopping time or an adapted random probability measure. These stopping times (or adapted random probability measures) follow a given distribution and can depend on the payouts. Our target is to deduce the estimation of the worstcase situation, that means, the supremum of the expected payout over all stopping times satisfying the given marginals. We formulate our task as an optimal transport problem and prove the existence of an optimal strategy by using the methods and techniques from the optimal transport theory.

Wednesday 14th November 2018  Cointegration in continuous time for factor models
Speaker: Prof. Fred Espen Benth (University of Oslo)
14:00PM Room: MATH105
Abstract: We develop cointegration for multivariate continuoustime stochastic processes, both in finite and infinite dimension. Our definition and analysis are based on factor processes and operators mapping to the space of prices and cointegration. The focus is on commodity markets, where both spot and forward prices are analysed in the context of cointegration. We provide many examples which include the most used continuoustime pricing models, including forward curve models in the HeathJarrowMorton paradigm in Hilbert space.

Wednesday 7th November 2018  Integrated Unit Linked Collective Assets (ICA)
Speakers: Cordelia Rudolph and Axel Helmert (MSG Life Austria)
16:00PM Room: MATH105
Abstract: The situation of life insurance companies and pension providers is challenging. One of the most difficult aspects is the low interest rate challenge. Together with the increasing requirements on solvency and other regulations this is developing pressure in search of new solutions. We have seen many attempts adopting long term guarantees in various new products, the results are not satisfying. In recent years, the opinion has prevailed that we need a more general approach. This leads us to the following questions: Is it possible to provide a high level of security combined with acceptable yields without traditional long term guarantees? Could we bring together the advantages of individual unit linked life insurance products with the traditional collective approach in a cost efficient automated environment?

Wednesday 24th October 2018  Trends in the extreme value index
Speaker: Prof Laurens de Haan, (Erasmus University Rotterdam, The Netherlands)
14:00PM Room: MATH105
Abstract: The first part of the talk will be an introduction to extreme value theory. I shall discuss the theoretical background, the tools for application and several specific applications.
A discussion of recent research follows. We consider extreme value theory for independent but not identically distributed observations. In particular, the observations do not necessarily share the same extreme value index. Assuming a continuously changing index we provide a nonparametric estimate for the functional extreme value index. Besides estimating the extreme value index locally, we also provide a global estimator for the trend and its joint asymptotic distribution. The asymptotic theory for the global estimator can be used for testing a predefined parametric trend in the index. In particular it can be applied to test whether the index remains constant across all observations. (Joint work with Chen Zhou).

Wednesday 17th October 2018  Optimal control of piecewise deterministic processes (PDP's)
Speaker: Dr Alexey Puinovskiy, (University of Liverpool)
14:00PM Room: MATH105
Abstract: PDPs are widely used in Insurance, Reliability, Mathem. Epidemiology, Queueing Theory and so on. For the standard discounted model with a single objective, Dynamic Programming approach proved to be successful. In the case of several objectives (constrained model), Linear Programming is more appropriate. In this talk I will explain some theoretical results in these areas obtained jointly with Prof. F. Dufour (INRIA, France) and Prof. O. Costa (Uni. Of Sao Paolo, Brazil): SIAM J. Control Optim, 2016, V.54, N.3, p.14441474. If time permits, I will also mention the so called impulsive control theory. Where possible, the connection to insurance will be demonstrated.

Wednesday 10th October 2018  Existence and Properties of Optimal Strategies for DistributionConstrained DiscreteTime Optimization Problems
Speaker: Uwe Schmock, (TU Wien  Technical University of Vienna)
14:00PM Room: MATH105
Abstract: We consider stochastic optimization problems in discrete time under distributional constraints. These problems are motivated by actuarial science, in particular to treat unitlinked insurance products with guarantees. They can also serve as benchmark models to account for customer behaviour, when the treatment as American option is not appropriate.
The basic mathematical setup is an adapted stochastic process (interpreted as payouts) and (possibly randomized) stopping times to optimize the expected payout. The difference to classical optimal stopping problems is our constraint concerning the distribution of the stopping times or, more generally, the adapted random probability measures.
For these distributionconstrained optimization problems we prove the existence of an optimal strategy, the basic assumptions are suitable moment conditions. In special cases, optimal strategies are identified explicitly. (The talk is based on joint work with Christiane Elgert and Karin Hirhager.)

Thursday 13th September 2018  Numerical methods for McKeanVlasov equations: taming, Importance Sampling & LDP's
Speaker: Goncalo dos Reis (University of Edinburgh)
15:00PM Room: 126 Mount Pleasant, Teaching Room 209
Abstract: We present several recent results on numerical methods for McKeanVlasov stochastic differential equations (MVSDEs). Firstly on how to simulate MVSDEs with drifts of superlinear growth, then how to employ the wellknown Importance Sampling variance reduction technique for the simulation of certain quantities of interest involving expectations of the solution to MVSDEs.
The presentation combines several joint works with:
S. Engelhardt and G. Smith, Simulation of McKean Vlasov SDEs with super linear growth, (arXiv:1808.05530)
G. Smith and P. Tankov, Importance Sampling for McKeanVlasov SDEs, (arXiv:1803.09320)
W. Salkeld and J. Tugaut, FreidlinWentzell LDPs in path space for McKeanVlasov equations and the Functional Iterated Logarithm Law, (arXiv:1708.04961) 
Thursday 19th July 2018  Kendall Random Walks
Speaker: Prof. Barbara JasiulisGoldyn (University of Wroclaw, Poland)
14:00PM Room: MATH029
Abstract: In this talk we introduce the Kendall random walks and the corresponding renewal processes. We prove asymptotic properties for them using regularly varying functions techniques. Applications to insurance will be discussed.

Wednesday 30th May 2018  Ruin problem for correlated Brownian motions
Speaker: Lanpeng Ji (University of Leeds)
14:00PM Room: MATH103
Abstract: Nowadays, insurance companies run different lines of businesses or collaborate with other companies, it is thus of interest to model these businesses using different risk processes, leading to the study of vectorvalued risk models. In this talk, we will focus on the most recent findings for vectorvalued Gaussian risk models. In particular, infinitetime simultaneous ruin probability of the (correlated) Brownian motions risk model will be discussed in detail, where we shall show the exact asymptotics of the ruin probabilities, by using the celebrated doublesum method combined with the theory of a quadratic programming problem. Additionally, the sojourn time of such risk model will be discussed, which has close relation with the Cumulative Parisian ruin, recently introduced in actuarial science.
This talk is based on joint works with Krzysztof Debicki (University of Wroclaw), Enkelejd Hashorva (University of Lausanne) and Tomasz Rolski (University of Wroclaw).

Wednesday 23rd May 2018  Portfolio Optimisation with Semivariance
Speaker: Kwok Chuen Wong (Dublin City University)
14:00PM Room: MATH103
Abstract: In this talk, I shall investigate dynamic portfolio management using semivariance of portfolio payoff as a portfolio risk measure. Comparing with variance which is widely used in the literature, semivariance is considered to be more plausible risk measure because semivariance penalizes adverse situations only. However, in the literature, it was shown that meansemivariance optimisation under the BlackScholes model has no optimal solution. Inspired by this nonexistence result, we replace the mean term with the expected value of utility satisfying the Inada conditions, then utilitysemivariance is solvable. By adding a downside risk management term such as semivariance, we numerically show that more than 90% of the respective deviation risk incured in the case of solely utility maximization can be reduced subject to less than 10% loss in utility as a tradeoff. Besides, I shall establish necessary and sufficient conditions under which the meansemivariance optimisation possesses an optimal solution; which generalises the negative result in the literature. Moreover, I shall suggest the models under which such sufficient conditions are satisfied, thus, under these models, the explicit optimal solution to meansemivariance optimisation can be obtained; such models can be applied into the themes of insurance and credit risk management. This talk is a joint work with Paolo Guasoni, Phillip Yam, and Harry Zheng.

Monday 14th  Thursday 17th May 2018  Allotey workshop: connecting Liverpool to Africa through mathematics and data science
This event is dedicated to the memory of Professor Francis Allotey. Professor Francis is well known for the “Allotey Formalism” in Xray spectroscopy. He obtained his master’s and doctorate degrees from Princeton University and Imperial College London, and he became the first Ghanaian full professor of mathematics at the Kwame Nkrumah University in 1974. He contributed to many international institutions including the Council of the prestigious Abdus Salam Centre since 1996. Among his many achievements for promoting science in Africa is his role in establishing AIMS Ghana in 2012.

Wednesday 9th May 2018  Indifference pricing of life insurance contracts via BSDEs under partial information
Speaker: Katia Colaneri (University of Leeds)
14:00PM Room: MATH103
Abstract: In this paper we investigate the pricing problem of a pure endowment contract when the insurer has a limited information on the mortality intensity of the policyholder. The payoff of this kind of policies depends on the residual life time of the insured as well as the trend of a portfolio traded in the financial market, where investments in a riskless asset, a risky asset and a longevity bond are allowed. We propose a modeling framework that takes into account mutual dependence between the financial and the insurance markets via an observable stochastic process, which affects the risky asset and the mortality index dynamics. Since the market is incomplete due to the presence of basis risk, in alternative to arbitrage pricing we use expected utility maximization under exponential preferences as evaluation approach, which leads to the socalled indifference price. Under partial information this methodology requires filtering techniques that can reduce the original control problem to an equivalent problem in complete information. Using stochastic dynamics techniques, we characterize the value function as well as the indifference price in terms of the solution to a quadraticexponential backward stochastic differential equation. This is a joint work with Claudia Ceci and Alessandra Creatarola.

Wednesday 2nd May 2018  Some challenges in portfolio optimization
Speaker: Bogdan Grechuk (University of Leicester)
14:00PM Room: MATH103
Abstract: Portfolio optimization is the process of finding the proportions of various financial instruments to form a portfolio, which is better than any other feasible portfolio according to some criterion/criteria. The main challenges in portfolio optimization are (i) it is unclear which criteria to use; (ii) not only future rates of returns of financial instruments are unknown, but their distributions are unknown as well; (iii) for a group of individuals with different investment preferences, optimal group portfolio is not the sum of individual portfolios. In this talk, some new approaches for addressing these challenges will be discussed.

Wednesday 21st February 2018  Determinants of tail risk in emerging and developed markets
Speaker: Devraj Basu and Bertrand Groslambert (Strathclyde University)
14:00PM Room: MATH103
Abstract: We study the distribution of extreme events risk across emerging and developed stock markets and empirically identify the determinants of tail risk across countries. A recent literature has shown that rare disasters can explain some of the most important puzzles in finance and that tail risk is priced in the cross section of asset returns. We find a strong empirical relationship between tail risk and the quality of institutions even after economic and financial variables have been accounted for. Better governance substantially reduces the probability of extreme events. In addition, we find that what differentiates developed and developing countries concerning extreme stock market risk is the quality of their institutions, not the depth of their financial markets, nor the degree of financial and trade openness.

Wednesday 7th February 2018  Spectral Backtests of Forecast Distributions with Application to Risk Management
Speaker: Alex McNeil (University of York)
13:00PM Room: Risk Institute Seminar Room
Abstract: In this talk we study a class of backtests for forecast distributions in which the test statistic is a spectral transformation that weights exceedance events by a function of the modelled probability level. The choice of the kernel function makes explicit the user's priorities for model performance. The class of spectral backtests includes tests of unconditional coverage and tests of conditional coverage. We show how the class embeds a wide variety of backtests in the existing literature, and propose novel variants as well. We assess the size and power of the backtests in realistic sample sizes, and in particular demonstrate the tradeoff between power and specificity in validating quantile forecasts.

Wednesday 31st January 2018  The Wilkie Model – Past, Present and Future
Speaker: Professor David Wilkie (HeriotWatt University)
14:00PM Room: MATH103
Abstract: David Wilkie, originator of what actuaries have come to call “The Wilkie Model”, will describe, briefly, how it originated, how it has developed, and what future developments are being considering for it.

Wednesday 15th November 2017  A test for the rank of the volatility process
Speaker: Prof Mark Podolskij (Aarhus University, Denmark)
14:00PM Room: MATH103
Abstract: In this talk we present a test for the maximal rank of the matrixvalued volatility process in the continuous Ito semimartingale framework. Our idea is based upon a random perturbation of the original high frequency observations of an Ito semimartingale, which opens the way for rank testing. We develop the complete limit theory for the test statistic and apply it to various null and alternative hypotheses. This is joint work with Jean Jacod.

Friday 10th November 2017  RELAX Actuarial Workshop
Venue: 128 Mount Pleasant
Speaker: Veronique MaumeDeschamps (Universite Lyon)
11:00  On some nonparametric methods for extensions of spatial maxstable processes
Speaker: Manuel Morales (University of Montreal)
11:30  On an Agentbased Simulator Model for the LimitOrderBook and its Applications to Measuring Price Impact
Speaker: Andrei Badescu (University of Toronto)
12:00  An IBNRRBNS insurance risk model with marked Poisson arrivals
12:30  Lunch
Speaker: Alfredo Egidio Dos Reis (University of Lisbon)
13:30  Estimation of foreseeable and unforeseeable risks

Friday 26th May 2017  A probabilistic approach to spectral analysis of growthfragmentation equations
Speaker: Alexander Watson (University of Manchester)
2:00PM Room: MATH104
Abstract: The growthfragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this talk, I discuss a probabilistic approach to the study of this asymptotic behaviour. The method is based on the FeynmanKac formula and the identification of a driving Markov process. This is joint work with Jean Bertoin.

Friday 26th May 2017  Beyond the Variance Risk Premium: Stock Market Index Return Predictability and OptionImplied Information
Speaker: Gabriel J. Power (Laval University)
10:30AM Room: Chadwick Building Seminar Room
Abstract: We investigate international stock market index return predictability using optionimplied information (SP500, DAX, FTSE, CAC, and SMI). We document the predictive power of several forwardlooking variables such as the variance risk premium and the FosterHart (FH) risk measure for horizons ranging from one to 250 days. Our results from predictive regressions as well as outofsample forecast tests suggest that the variance risk premium is a significant predictor of returns at horizons below one month, in addition to the previously documented quarterly predictability. FosterHart riskiness also has significant forecasting power for longer horizons. Overall, our results show that the VRP and FH risk are complementary. Riskneutral skewness and kurtosis are often significant in predictive regressions, but in outofsample lose significance once VRP and FH are introduced in the model.

Friday 12th May 2017  Eddie Stobart: what we do, our challenges, what data we collect
Speaker: Dr. Damon Daniels, Strategic Network Manager, Eddie Stobart
12:00PM MATH104
Abstract: Damon (Liverpool alumus) will talk about how he came to at Eddie Stobart, and the beginnings of him trying to bring in some new approaches to the road network (some first steps analysis he did, and the tolls/methods he used that he picked up from his PhD). He will summarise the partnerships first project with Suhang Dai; the problem they had, and how working with Suhang has led to measureable business improvements for Eddie Stobart. Finally, outlining the future partnership plans; with big emphasis on potential projects they are hoping to develop across their Commercial, Finance, Operations and Network teams.

Friday 5th May 2017  Forecasting algorithms for recurrent patterns in consumer demand
Speaker: Oleg Karpenkov, University of Liverpool
3:00PM MATH106
Abstract: In this talk we discuss a new forecasting algorithm for recurrent patterns in consumer demand. We study this problem in two different settings: refill and supply models. We will consider several features of the algorithm concerning sampling, periodic approximation, denoising and forecasting. This is a joint research together with T.Boiko and B.Rakhimberdiev.

Friday 24th March 2017  Lifetime Dependence Modelling using a Generalized Multivariate Pareto Distribution
Speaker: Dr. Daniel Alai, University of Kent
2:00PM RENSR1 (Rendall Building Seminar Room 1)
Abstract:
An important driver of longevity risk is uncertainty in oldage mortality, especially surrounding potential dependence structures. We investigate a multivariate Pareto distribution that allows for the exploration of a variety of applications, from portfolios of standard annuities to jointlife annuity products for couples. In past work, it has been shown that even a little dependence between lives can lead to much higher uncertainty. Therefore, the ability to assess and incorporate the appropriate dependence structure, whilst allowing for extreme observations, significantly improves the pricing and risk management of lifebenefit products. Finally, we explore a generalization of the multivariate Pareto distribution via established links with Archimedean survival copulas.Based on joint work with Profs Zinoviy Landsman and Michael Sherris. 
Thursday 16th March 2017  Asymptotic hedging of barrier option via parametrix and FourierMalliavin estimators based on discrete measures
Speakers: Dr Yuri Imamura, Tokyo University of Science and Dr. Nienlin Liu, Ritsumeikan University, Japan
1:00PM GUILDSUTC

Friday 10th March 2017  On subexponential tails for negatively driven compound renewal processes with application to twodimensional ruin problem
Speaker: Prof Dima Korshunov, Lancaster University
10:00AM GUILDSUTC
Abstract: We discuss subexponential tail asymptotics for the distribution of the maximum $M_t:=\sup_{u\in[0,t]}X_u$ of a process $X_t$ with negative drift for the entire range of $t>0$. We consider compound renewal processes with linear drift and L'evy processes being motivated by Cram'erLundberg renewal risk process. These results allow to analyse the asymptotics of ruin probabilities of two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions when the initial reserves of both companies tend to infinity and generic claim size is subexponential. (Particularly based on a joint work with Sergey Foss (Edinburgh) and Zbignew Palmowski (Wroclaw)).

Friday 10th February 2017  Exploiting Asymptotic Structure for Efficient Rareevent Estimation for Sums of Random Variables
Speaker: Thomas Taimre (The University of Queensland, Australia)
2:00PM MATH106
Abstract: We consider the problem of estimating the righttail probability of a sum of random variables when the density of the sum is not known explicitly, but whose asymptotic behaviour is known. We embed this asymptotic structure into a simple importance sampling estimator, in which we consider the radial and angular components of the distribution separately. By design, this estimator has a bounded relative error when the marginal tails decay exponentially. Moreover, we present a procedure to obtain a `good' approximation to the angular component as a mixture of Dirichlet distributions by using Bernstein polynomial approximation (cf. the Weierstrass approximation theorem). The estimator and procedure are applicable in both the heavy and lighttailed settings, as well as for dependent and independent summands. We illustrate the approach with a series of examples. This is joint work with Patrick Laub.

Wednesday 8th February 2017  An Endogenous RegimeSwitching ContinuousTime Diffusion Model for S&P 500 Volatility Index
Speaker: Jie Cheng
2:00PM MATH029
Abstract: We propose a new regimeswitching continuoustime diffusion model for S&P 500 Volatility Index (VIX). Our model may be regarded as an extension of Choi et al. (2015) who developed a noval endogenous regimeswitching mechanism for discretetime Gaussian processes where the switching between regimes is driven by a latent factor potentially correlated with the innovations of the observed time series. We allow our regimedependent diffusions to be continuoustime and nonGaussian by considering nonlinear transformations of underlying OrnsteinUhlenbeck (OU) processes, whereby the switching of regimes is driven by a latent factor potentially correlated with the innovations of the underlying OU processes. We apply the proposed model to time series of VIX at monthly, weekly and daily frequencies. In addition to .finding strong evidence of regime switching effect and endogeneity in the switching of regimes, we are also able to extract the latent factor that drives the switching of the regimes for further analysis. Our model appears to perform better for VIX at monthly and weekly frequencies than at daily frequency.

Wednesday 1st February 2017  Ruin probabilities: exact and asymptotic results
Speaker: Prof. Zbigniew Palmowski, Wroclaw Technical University, Poland
2PM MATH106
Abstract: Ruin theory concerns the study of stochastic processes that represent the time evolution of the surplus of a stylized nonlife insurance company. The initial goal of early researchers of the field, Lundberg (1903) and Cramér (1930), was to determine the probability for the surplus to become negative. In those pioneer works, the authors show that the ruin probability decreases exponentially fast to zero with initial reserve tending to infinity when the net profit condition is satisfied and clam sizes are lighttailed.
During the lecture we explain when and why we can observe this phenomenon and discuss also the heavytailed case. We demonstrate main techniques and results related with the asymptotics of the ruin probabilities: PollaczekKhinchin formula, Lundberg bounds, change of measure, WienerHopf factorization, principle of one big jump and theory of scale functions of Lévy processes.

Wednesday 25th January  Time fractional diffusion systems and their applications in control theory
Speaker: Prof. Chunhai Kou (College of Science, Donghua University, Shanghai)
2:00PM Seminar Room 4 (JSMSR4), Muspratt Building
Abstract: Recently anomalous diffusion systems have attracted increasing research interest since the introduction of continuous time random walks (CTRWS) and a large number of contributions have been given to them. The time fractional diffusion system, which replaces the first order time derivative by a fractional derivative, has been seen as the macroscopic presentation of a CTRW model. From a physical viewpoint, this generalized diffusion equation can be used to describe transport processes with long memory in the spatially inhomogeneous environment. Here we attempt to explore the boundary feedback stabilization for a class of time fractional diffusion systems. By designing an invertible coordinate transformation, the MittagLeffler stability of the system studied is obtained. Simulation result is also given at last to test the effectiveness of our results. We hope that the results here could provide some insight into the control theory analysis for the time fractional diffusion system.

Thursday 1st December  Parisian ruin theory for Lévy insurance risk processes
Speaker: JeanFrançois Renaud (UQAM)
3:00PM Room G16
Abstract: In the last few years, the idea of Parisian ruin has attracted a lot of attention. In Parisiantype ruin models, the insurance company is not immediately liquidated when it defaults: a grace period is granted before liquidation. Roughly speaking, Parisian ruin occurs if the time spent below a predetermined critical level is too long. In this talk, I will present recent results related to different definitions of Parisian ruin for spectrally negative Lévy processes.

Thursday 24th November 2016  Ruin probabilities in Gamma risk models
Speaker: Wei Zhu (University of Liverpool)  RARE Seminar
3:00PM Room 201 Electrical Engineering
Abstract: In risk theory, the classical risk model assumes that each claim arrives after an exponential time. This talk considers a generalization of the exponential interclaim times assumption of the classical model. Specifically, when the waiting times are Gamma distributed, we show that the ruin probability satisfies a fractional integrodifferential equation, which has explicit solutions under certain assumptions on the claim size distribution.
The RARE (Risk Analysis, Ruin and Extremes) project supported by the EU Marie Curie International Research Staff Exchange Scheme has ran for 4 years (Dec 1, 2012 Nov 30, 2016) and has covered over 400 months of travel exchanges between 12 partner universities. IFAM has coordinated this project and benefited greatly from this network exchanges. Over 200 publications have been produced as result of this project.

Thursday 20th October 2016  A dual parameter longmemory model
Speaker: Professor Rajendra Bhansali (University of Liverpool)
2:00PM Room MATH027
Abstract: A new model for longmemory time series is introduced. It involves two memory parameters, d and c , say, and characterizes the correlation decay as a mixture of polynomial and logarithmic rates . This model includes as its special case the standard long memory model with a single memory parameter, d , in which the correlations decay only at a polynomial rate. Examples illustrating some situations in which the standard model does not apply but the new model does do so are presented. A mathematical definition of the class of dual parameter long memory models is given and this class is extended to include also the class of dual parameter intermediate memory models. The class of parametric dualparameter FARIMA models, called DFARIMA models, is also introduced and the notions of strong, weak and mixed long and intermediate memory are defined. Nonparametric and semiparametric estimation of the parameters of the new model by the dual parameter extensions of the standard logperiodogram and local Whittle methods is considered together with the maximum likelihood estimation of the parameters of the DFARIMA model. Asymptotic properties of the estimates are investigated and it is shown that the standard singleparameter estimation methods can be badly biased when the dual parameter model holds. The usefulness of the asymptotic results for observed series of finite length is investigated by a simulation study. An application of the dual parameter model to internet packet traffic is also discussed.

Thursday 22nd September 2016  On the Fatou property of convex functions on the duals of Orlicz spaces
Speaker: Dr. Keita Owari (Ritsumeikan University, Japan)
4:00PM Room 103

Wednesday 9th March 2016  Herdlike Behaviour and the Psychology of Market Bubbles
Speaker: Colm Fitzgerald
15:00  Lecture Theatre 2 Life Sciences
Lecture sponsored by the Worshipful Company of Actuaries
Colm Fitzgerald will discuss methodologies that can be used to assess and manage various forms of risks related to group psychology, e.g. herdlike behaviour, financial market bubbles, etc. He will use the concept of the narrative, draw the distinction between a narrative and an analysis and will use this approach to define what he refers to as 'narrative risk'. He will look back at historical bubbles to point out what we can learn and what we cannot learn from them. He will also discuss probable current bubbles.
Colm is a Fellow of the Institute & Faculty of Actuaries and the Society of Actuaries in Ireland. He lectures in actuarial science in University College Dublin and is a member of the Education Board and the Board of Examiners of the Institute & Faculty of Actuaries. Previously, he spent most of his career working as a trader, finishing up as Head of Quantitative Trading in Bank of Ireland Global Markets. His research interests include the psychology of risk, trading models, the application of actuarial techniques in wider fields, applying classical thought and forestry.
Timetable
 15:00  15:15 Opening remarks
 15:15  16:00 Presentation by Colm Fitzgerald
 16:00  16:30 PhD and UG students’ presentations
 16:30  16:35 Prizes
 16:35  17:00 Coffee and posters

Monday 7th March 2016  Tail process and extremes of heavy tailed sequences
Speaker: Prof. Bojan Basrak (University of Zagreb, Croatia)
3:00PM, Lecture Theatre 029
Abstract: We describe how one can characterise dependence structure in a stationary heavy tailed sequence using the notion of tail process. This theory is applied to study extreme values of dependent regularly varying sequences, such as GARCH processes for instance. We will also discuss the convergence of partial sums and corresponding point processes, covering some recent results in the literature.

Tuesday 1st March 2016  RARE workshop on Stochastic Analysis and Applications
As part of the Risk Analysis, Ruin and Extremes (RARE EUIRSES 318984) project, we are pleased to host a one day workshop at the University of Liverpool.
Programme
 09:00  09:30 Welcome  Coffee at Victoria Gallery and Museum
Morning Session (Seminar room 521, Cedar House)
 09:30  10:15 Andrea Macrina (University College, London)
 10:15  10:45 Camilo Garcia Trillos (University College, London)
 10:45  11:15 Coffee at Victoria Gallery and Museum
 11:15  12:00 Mihalis Zervos (London School of Economics)
 12:00  12:30 Yuri Imamura (Ritsumeikan University, Japan)
 12:30  14:00 Lunch at Victoria Gallery and Museum
Afternoon Session (Lecture room 203 (E3) Electrical Engineering)
 14:00  14:45 Kai Liu (University of Liverpool)
 14:45  15:15 Zhongyang Sun (Nankai University, China)
 15:15  15:45 Coffee at Victoria Gallery and Museum
 15:45  16:30 Toshihiro Yamada (Tokyo University, Japan)
 16:30  17:00 Alexey Piunovskiy (University of Liverpool)
This workshop has received funding from the European Union’s Seventh Framework Programme for research, technological development and demonstration under grant agreement no 318984 –RARE