Specific Research Areas

The research of the Institute members focuses on actuarial and financial mathematics and its mathematical foundations.

  • Advanced ruin theory
  • Dividend problems in insurance
  • Derivative pricing
  • Stochastic differential equations
  • Stochastic and deterministic control theory
  • Nonlinear stochastic and deterministic partial differential equations
  • Interest rate derivatives and term structure models



Past Grants

How do economic variables affect the pricing of agricultural commodity derivatives and insurance?

Granting Agency: Montreal Institute of Structural Finance and Derivatives

This project, by applying novel mathematical tools and based on the applicants’ expertise on the field of derivatives, insurance, and risk management including application to commodities, aims to study the pricing of agricultural commodity derivatives and insurance as part of a larger risk mitigation program in the agricultural sector.

Date: 2017
Principal Investigator: Dr. Hirbod Assa.
Co-PI: Gabriel Power and Philippe Gregoire (Laval University)
Beneficiaries: PhD Students, PI and Co-PI's.
Amount: 50K CAD

RARE - Risk Analysis, Ruin and Extremes

Granting Agency: FP7 -  Marie Curie People Action
Scheme: International Research Staff Exchange Scheme (IRSES)

This project, aims to develop the theoretical side of the analysis of ruin probabilities in case of disasters or extreme shocks for insurance-like risk pools. It will investigate two major themes: Risk Modelling and New Developments on Extremes and Rare Events. The project aim is to address rare events and extremes by analysing environmental and financial risks using probabilistic tools.

Since specialists working on the areas of extremes and rare events are scarce and sparse, such an exchange program helps to create a network of knowledge, ideas and experience. The project  intends to create an initial worldwide network by supporting regular exchange between researchers from the 12 participating institutions from the UK, Switzerland, France, Poland, Russia, India, China, Japan, Australia and the USA.

Duration: 4 years
Start Date: December 1, 2012
Partners: ESSEC Paris (France), University of Lausanne (Switzerland), ETH Zurich (Switzerland), University of Wroclaw (Poland), ISI Calcutta (India), IIMB Bangalore (India), Moscow State University (Russia), Nankai University (China), Monash University (Australia), Ritsumeikan University (Japan), University of Nevada at Reno (USA)
Scientific Coordinators: Prof. Marie Kratz (ESSEC), Prof. Enkelejd Hashorva (University of Lausanne)
Project Coordinator:  Dr. Corina Constantinescu (IFAM, University of Liverpool)

Agricultural insurance and reinsurance

Granting Agency: Society of Actuaries
Scheme: Individual grants competition

The aim of this project is to introduce advanced methodologies, either mathematical or numerical, for pricing agricultural insurances and designing efficient reinsurance policies. The target is to provide necessary tools and create necessary knowledge for the practitioners and the policy-makers, as well as for the academic body involved in the area of agricultural finance and insurance.

Duration: 1 year
Start date: April 1st, 2015
Principal Investigator: Dr. Hirbod Assa and Dr. Thanasi Pantelous.
Grant Beneficiary: Meng Wang

Automatic Balancing Mechanisms in PAYGO Pension Systems

Granting Agency: Investment & Pension Europe
Scheme: IPE Scholarship Fund Award

The common trend in responses to what is a pensions crisis is a wave of parametric pension adjustments during the last years in countries like France, Greece, Hungary, Japan, Romania and Spain. These parametric reforms include, among others, changes in the contribution ceilings, increases in the retirement age, reductions in the indexation of pensions or even carrying out a structural reform from a Defined Benefit PAYGO pension system to a Notional Defined Contribution or even to a funding pension schemes such as Chile, Czech Republic, Mexico, Hungary among others. Following this process of reforming the pension system, my thesis is focused on one of the most important innovation in public pension schemes over the past years, Actuarial Balancing Mechanisms (ABM) in PAYGO. The project has two main objectives:

  1. To design an automatic balancing mechanism to restore the sustainability of Pay-As-You-Go pension system based on minimizing changes in the main variables, such as the contribution rate, normal retirement age and indexation of pensions. This mechanism, that uses an intertemporal optimization model, identifies and applies an optimal path of these variables into a PAYGO system and absorbs fluctuations in longevity, fertility rates, life expectancy, salary growth or any other random events in a pension system. The main purposes of the ABM, through successive application, are to re-establish the financial equilibrium of PAYGO adapting the system to changes in socio-economic and demographic conditions; to create a credible institutional framework to increase the likelihood that promises of pension payments will be respected; and to minimize the use of the pension system as an electoral tool.
  2. To analyse the robustness of the automatic balancing mechanism by means of different population structures, investment rates and replacement rates, among others. Furthermore, our ABM can be easily generalised to include more parameters and is applicable to any PAYGO pension system.

Duration: 1 year
Start date: June, 2015
PhD student supervisor: Dr. Carmen Boado-Penas.
Grant Beneficiary: Humberto Godínez Olivares.


Granting Agency: FP7 - Marie Curie People Action
Scheme: Greek/Regional Fund - Archimedes III

The main objective of this research proposal is to extend existing numerical and symbolic methods for solving problems in polynomial linear systems theory, by investigating new approaches at both theoretical level and in terms of implementation in popular computational environments of numerical or symbolic mathematical processing. The research interest in the analysis and synthesis of multivariable control systems standards-based systems (see Baras 1991), known in the literature as Polynomial Matrix Descriptions (PMDs) launched forty years ago at the University of Manchester Institute of Science and Technology (UMIST) from the founder and director of the Control Systems Centre UMIST Prof. F.R.S. Rosenbrock and his colleagues. Rosenbrock, in a number of pioneering theoretical results that appeared in a number of publications and books (Rosenbrock 1970, 1974) laid the foundations of the problems of analysis and synthesis of multivariable control systems by polynomial matrices (Polynomial Matrix Approach), generalizing the very popular in the U.S., through the work of R.E. Kalman (1969), state space theory. Important theoretical results, extending and completing the "polynomial theory" of Rosenbrock published later by Wolovich (1974) and his colleagues and later by Kailath (1980) and his colleagues in Verghese (1978), in Kucera (1979 ), the Blomberg H. and Ylinen (1983), Vidyasagar (1985), the Vardulakis (1991) etc. Over the past forty years, the description of multivariable polynomial systems, also known as "algebraic approach", has prevailed as a very active research area.

The results of the proposed project are expected to contribute to the education foundation of both field control engineers and control theorists, by furthering the available curriculum on methods for analysis and design of linear and nonlinear systems. The communities that will benefit from the results of the proposed research project are:

• Academic research groups working in areas related to the subject of the project
• Research laboratories working on control or signal processing applications
• Industry with interest in control applications (process control, automotive, aerospace, etc)
• Industry with interest in signal processing applications (telecommunications, networks, image processing, finance etc)

Duration: 3 years
Start date: December 1st, 2012
Partners:  Technological Educational Institute of Thessaloniki (ATEITH), Aristotle University of Thessaloniki (AUTH) (Greece) and University of Liverpool (UOL) (UK)
Project Coordinator:  Dr Efstathios Antoniou (Department of Sciences, Alexandrian Technological Educational Institute of Thessaloniki (ATEITH)
External Coordinator: Dr Athanasios Pantelous (IFAM, University of Liverpool)

Granting Agency: Engineering and Physical Sciences Research Council (EPSRC) Scheme: Shaping Capability Funds

The proposed activities are geared towards identifying novel approaches to analysing the spread and consequently the financial risk of skin cancer in UK.  The analysis builds on the cross-disciplinary interaction and collaboration between the Department of Mathematical Sciences and medical doctors from the University Hospital of North Staffordshire. These activities are intended to establish wider long-term collaborations between the two organisations.
Duration: 1 year
Start date: April 1st, 2012
Partner: University Hospital of North Staffordshire
Partner Coordinator: Dr. Sanda Popescu (University Hospital of North Staffordshire)
Project Coordinators: Dr. Kieran Sharkey and Dr. Corina Constantinescu (University of Liverpool)

Granting Agency: Business Gateway - University of Liverpool
Scheme: KE Vouchers

For insurance companies, selecting strategies to manage the risk is a complex process. On the quantitative side, companies are keen to understand the risk-return dynamics of alternative strategies. As the recapitalization tends to be expensive, it is important to identify the processes under which the capital can be eroded by claims. Risk theory is designed to answer questions in this area. Based on recent research, there are new approaches available to model these risk-return dynamics (see Constantinescu et.al.). The urgency of enhanced ways to asses risk and return is raised by the forthcoming Solvency II regulation, guaranteeing the timeliness of the project.

This project is designed to be conducted by MSc students from the Financial Mathematics Master program, supervised by IFAm staff (Dr. Corina Constantinescu, Dr. Olivier Menoukeu-Pamen, Dr. Apostolos Papaioannou, Dr. David Siska) with input from Aspen (Dr. Joseph Lo).

Duration: 6 months
Start date: February 15th, 2013
Partner: Aspen (London)
Partner Coordinator: Dr. Joseph Lo (Aspen)
Project Coordinator:  Dr. Corina Constantinescu (IFAM, University of Liverpool)


Granting Agency: University of Sao Paulo, Brazil - University of Liverpool
Scheme: Science without borders

The two collaborating groups will concentrate their combined research in three directions. The first direction is the investigation of the effect on consumption of the heterogeneity of social susceptibility of consumers. Second, the stability of consumption processes will be analyzed by appropriate stochastic dynamical system model of social consumption. Third, the leverage effect in financial time series will be studied from the perspective of its effect upon the asymmetry between the inverse statistics of gain and of loss of financial investments. The three topics are totally novel. The results are expected to allow for the control of real world socio-economic systems so as to put them in the (robustly) stable state.

The Sao Paulo group will contribute with statistical inference at phenomena to be studied, construction of mathematical model and their rigorous study. The experience of the Liverpool University group will help to identify phenomena at the interface between complex socioeconomic systems and phenomena arising in the insurance (PAYGO social security schemes – Pension plans) and similar socio-economic environments.

Duration: 1 year
Start date: September 1st, 2012
Partner Coordinator: Dr Vladimir Belitsky (USP)
Project Coordinator:  Dr Athanasios Pantelous (IFAM, University of Liverpool)

Granting Agency: University of Liverpool
Scheme: Practice

Analysis of Correlation Based Networks Representing DAX 30 Stock Price Returns (Ms Jenna Birch - FNA, Dr. Kimmo Soramaki, Founder and CEO of FNA, kimmo@soramaki): We aim to write a project report detailing how network theory can be used to model the correlation between stocks on the DAX30 and compare the varies network structures that can be used. FNA can be used to create these network structures as well as perform the statistical analysis. As FNA is constantly developing this is also an opportunity to test the platform on real data.

Optimal strategies for long-term sustainability in Pensions Plans using control theory in a dynamic nonlinear system framework (Mr Humberto Godinez Olivares - Petroleos Mexicanos): Applying control theory and forecasting techniques, the main objective of the project is to design the optimal contribution rate, age of normal retirement and investment strategy in a Pensions Plans in order to guarantee long-term stability for the Pension System.

Pricing Bonus Malus systems by calibrating the market data via a ruin probability approach (Ms Weihong Ni - Aspen Insurance UK Ltd, Dr. Joseph Lo, Head of Actuarial Research & Development, joseph.lo@aspen.co): There are clear connections between the calculation of ruin probabilities and the stationary distributions of Bonus-Malus Systems. This project attempts to test this connection on real data. The partnering insurance company disposes of large data sets on which such analysis is possible. Thus, in addition to the aforementioned “calibrating new default risks models to market data” project, this will provide a short cut to modelling a Bonus Malus system price for large claim amounts.

Optimal pricing strategies for an insurer in a competitive market (Mr John McCarthy, FIA - RSA, Rachael Larkin, Deputy Actuarial Manager, Rachael.Larkin@uk.rsagroup.com): We would like to (a) produce a report summarising the current academic perspective on this topic, (b)to set up a contact with RSA for future engagement, and (b) identify and discuss opportunities for future engagement with RSA 

Duration: 6 months up to 1 year
Start date: February 1st, 2013
PhD students supervisors: Dr Athanasios Pantelous, Dr Corina Constantinescu (IFAM), and Dr. Ioannis Kougioumtzoglou (IR&U)