1.    Provide a solid grounding in analysis of general insurance data,Bayesian credibility theory and the loss distribution concept.

2.    Provide an introduction to statistical metho ds for managing risk innon-life insurance and finance.

3.    Prepare the students adequately to sit for the exams of CT6 subject ofthe Institute of Actuaries.

Be able to apply the estimation methods described in (b) of the Syllabus for the distribution described in (a) of the Syllabus, be able to make hypothesis testing described in (b) of the Syllabus for the distribution described in (a) of the Syllabus.

Be able to estimate the parameters of the loss distributions when data complete/incomplete using the method of moments and the method of maximum likelihood, be able to calculate the loss elimination ratio.

Understand and use the Buhlmann model, the Buhlmann-Straub model, be able to state the assumptions of the GLM models – normal linear model, understand the properties of the exponential family.

Be able to express the values of the life assurances in (d) of the Syllabus and the life annuities in (f) of the Syllabus in terms of the life table functions. Be able to use approximations for the evaluation of the life assurances in (d) of the Syllabus and the life annuities in (f) of the Syllabus based on a life table.

Be able to describe the properties of a time series using basic analytical and graphical tools.

Understand the definitions, properties and applications of well know time series
models, fit time series models to practical data sets and select the suitable models, be able to perform simple statistical inference (forecasting) based on the fitted models, estimate and remove possible trend and seasonality in a time series, analyse the residuals of a time series using stationary models.

(a) Review of probability theory and Statisticalinference
Estimation, method of moments, unbiasedness, the likelihood function andmaximum
likelihood estimation, confidence interval for the population mean difference,hypothesistesting, the exponential, gamma, log-gamma, Pareto, generalizedPareto, normal, lognormal,Weibull, Burr, log-logistic, Benktander IIdistributions, comparison of the tails of distributions (asymptotictechniques), mixing distributions.

(b) Loss distribution
Moment generating functions (if exists), moments, the variance and alternativemethods for the calculation of moments when the moment generating function doesnot converge for the distributions described in (a) of the Syllabus, theKolmogorov – Smirnov test, the likelihood ratio test.

(c) Special types of insurance schemes &Reinsurance
Define simple insurance schemes due to deductibles and retention of limits,policy limits, proportional reinsurance, excess of loss reinsurance,statistical inference for the previous insurance/reinsurance schemes with themethods in the in (b) of the Syllabus.

(d) Bayesian statistics and credibility theory
The Bayes Theorem and conditional probabilities, the prior and the posteriordistribution, conjugate prior distributions and the linear exponential family,the loss function, the credibility premium, the credibility factor, theBuhlmann model, the Buhlmann-Straub model, exact credibility.

(e) GLM
Linear regression, the multiple linear regression, the normal linear model,GLM: the exponential family of distributions for the binomial, Poisson,exponential, Gamma, normal distribution, the Pearson and deviance residuals,application of tests in model fitting.

(f) Simulation
The basic of simulation, the simulation approach, the truly random and thepseudo random numbers, derivation/generation of the pseudo random numbers,applications to sets of simulation, Monte Carlo simulation, the number ofsimulations .

(g) Time Series with applications
Serial dependence (autocorrelation coefficients, correlograms), stationary andnon-stationary processes, filters and operators, Moving Average (MA) process(properties and applications), Autoregressive (AR) process (properties andapplications), Autoregressive moving average (ARMA) process (properties andapplications), extension to integrated (ARIMA) processes, non-linear processes,such as ARCH and GARCH, the multivariate autoregressive model,