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 methods for managing risk in non-life insurance and finance.

3. Prepare the students adequately to sit for the exams of CS2 subject of the Institute of Actuaries.

(LO1) Be able to apply the estimation methods described in (b) of the Syllabus, be able to make hypothesis testing described in (b).

(LO2) Be able to estimate the parameters of the loss distributions using the method of moments and the method of maximum likelihood, be able to calculate the loss elimination ratio.

(LO3) Be able to explain concepts of Bayesian statistics and calculate Bayesian estimators, understand and use the Buhlmann model, the Buhlmann-Straub model.

(LO4) Be able to state the assumptions of the GLM models - normal linear model, understand the properties of the exponential family.

(LO5) Be able to explain the concepts of Monte Carlo simulation.

(S1) Problem solving skills

(S2) Numeracy

(a) Review of probability theory and Statistical inference
Estimation, method of moments, unbiasedness, the likelihood function and maximum likelihood estimation, confidence interval and hypotheses testing.

(b) Loss distribution, survival analysis and heavy tails
Moment generating functions (if exists), moments, the Kolmogorov-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 the methods in (b) of the Syllabus.

(d) Bayesian statistics and credibility theory
The Bayes Theorem and conditional probabilities, the prior and the posterior distribution, conjugate prior distributions and the linear exponential family, the loss function, the credibility premium, the credibility f actor, the Buhlmann 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 the pseudo random numbers, derivation/generation of the pseudo random numbers, applications to sets of simulation, Monte Carlo simulation, the number of simulations.