Financial operations under certainty and uncertainty conditions. Financial markets and non-arbitrage principle. Portfolio selection. The concept of economic risk. Risk aversion: risky investments and insurance policies. Risk measures. VaR and Expected Shortfall. Introduction to the Extreme Value Theory. Financial and actuarial instruments for managing catastrophic risks.
1) L. Vannucci et al. - Metodi matematici e applicazioni economico-finanziarie, vol. 2 - Pitagora Editrice.
2) J. Ingersoll - Theory of financial decision making - Rowman & Littlefield
3) A. McNeil et al. - Quantitative risk management: concepts, techniques and tools - Princeton Series in Finance
4) P. Embrechts et al. - Modelling extremal events for insurance and finance - Springer
Introducing stochastic methods for financial and actuarial evaluations. Linking concepts and operations of risk pricing and risk managing: that is, showing how an actuary can become risk manager.
Probability and mathematics for statistics.
Classroom lectures: 72 hours.
Type of Assessment
Writen and oral examination. Two intermediate written tests will be proposed. One on financial mathematics arguments (interest rates, non-arbitrage prices, portfoilio selection); another one on risk analysis arguments (risk premiums, policy prices, risk measure computation).
1) Elementary financial mathematics. Financial operations and main financial regimes. Internal rate of return. Annuities and mortgages. Bond markets.
2) Financial mathematics under uncertainty. Stock markets. Non-arbitrage principle. Arrow securities. Risk neutral probability. Portfolio selection. Mean variance criterion. CAPM
3) Economic risk. Expected utility and risk aversion. Risk premium and insurance policy price. Regulatory capital and risk measures. VaR and Expected Shortfall.
4) Introduction to Extreme Value theory. Sub-exponential distributions. Limits of maximums. Extreme value distributions. Insurance and financial instruments to manage catastrophic risks.