1. P. Embrechts, R. Frey, A. McNeil – Quantitative Risk Management – Princeton University Press, 2015
2. P.J. Boland – Statistical and Probabilistic Methods in Actuarial Science – Chapman & Hall, 2011
3. P. Shevchenko - Modelling Operational Risk Using Bayesian Inference – Springer Verlag, 2011
How can a scholar of statistics, probability, actuarial science become a risk manger.? To this end the course wishes to provide both some instruments and some suggestions. The ultimate goal is to found an inventive and innovative practice on a solid and updated theoretical knowledge.
Probability and Mathematics for Statistics.
Lectures and laboratories.
Type of Assessment
Intermediate tests and final examination: written and oral tests.
1. Introduction to Quantitative Risk Management.
a) Definition of economic risk. Finance and insurance risks: examples.
b) The concept of risk aversion. Risk premium and insurance prices. HARA utility functions. Numerical examples.
c) The loss variable. Loss distribution for a risk portfolio. Portfolios of stocks, options, bonds, risky credits.
d) Risk measures. Value at Risk and Expected Shortfall. Basel and Solvency guidelines. Computational method for risk measures: Monte Carlo simulations and deterministic algorithms.
2. Probabilistic and statistical evaluation of risks.
a) Aggregate distributions of risks and their approximation.
b) Bayesian inference for loss distributions.
c) Models of risk dependence. Copulas through statistical inference.
3. Elements of Extreme Value Theory
a) Extreme values topics.
b) Probabilistic and statistical models of extreme risks: light and heavy distributions of losses. The ruin probability in the two cases.
c) Limits of sums and maxima.
d) The Fisher-Tippet theorem.
e) Generalized Pareto distribution: numerical cases.
4. Statistical, financial and actuarial tools for risk management
a) Financial products for environment risk prevention and mitigation: CAT bonds and project options. Data analysis and case studies: floods, earthquakes, drought.
b) Statistical evaluation of health risks. Public health care and private insurance. The mal-practice risk. Defensive medicine, insurance and litigation: evolutionary models.
c) Art and heritage risk management. Role of foundations. Insurance policies and ethical finance.