Finance and insurance

1. Introduction to risk management in insurance. Principles of premium calculation and their properties. Examples. Structure of claims. The random variable of aggregate claims cost. Calculation of the distribution function of aggregate claims cost. Calculation of moments. The random variable of the number of claims. Some explicit distributions: binomial distribution, Poisson distribution, finite mixture of Poisson. Compound distributions: compound binomial, compound Poisson. Calculation of expected value, variance, distribution function, and moment generating function of the aggregate claim. The random variable of single claim cost. Light-tailed and heavy-tailed probability distributions. Subexponential probability distributions. 2. Ruin theory. Discrete-time model. Probability of ruin in finite and infinite time. Net Profit Condition. The adjustment coefficient. Lundberg’s inequality. The classical model of collective risk theory. Renewal processes and their properties. Poisson and compound Poisson processes. Net Profit Condition. The adjustment coefficient. Lundberg’s inequality. Integro-differential equation for the probability of ruin. The case of exponential claims. 3. Introduction to reinsurance. Linear and non-linear forms of reinsurance. The Cramér–Lundberg model with reinsurance. Unilateral policies of optimal risk retention. 4. Introduction to risk measures. Value-at-Risk and Conditional Tail Expectation. Coherent risk measures. Examples. Theoretical lectures will be complemented by computer lab sessions on the following topics: - Simulation of random numbers and random variables - Light-tailed and heavy-tailed distributions - The random variable of the number of claims. Distribution of the number of claims for a risk portfolio. The random variable of single claim cost. - Calculation of the distribution function of aggregate claims cost - Simulation of the Cramér–Lundberg model, including with reinsurance - Simulation techniques for the calculation of risk measures, with particular focus on Value-at-Risk and Conditional Tail Expectation.

To successfully attend the course, students are expected to have basic knowledge of mathematics, elements of financial mathematics, introductory probability, and basic statistics.

- David C. M. Dickson, Insurance Risk and Ruin, Cambridge University Press - T. Mikosch, Non-Life Insurance Mathematics, Springer - Rob Kaas, Marc Goovaerts, Jan Dhaene, Michel Denuit, Modern Actuarial Risk Theory

Attendance is not mandatory, but it is strongly recommended.

Oral examination

Face-to-face lectures with examples and exercises. Computer lab sessions. The exercises will be implemented in MATLAB.