Actuarial models for life, disability and health insurance, mathematics for pensions, pension funds, healt insurance mathematics, unit-linked life insurance contracts.
(I) Insurance of several lifes, total loss in a portfolio, collective model, Panjer recursion, reinsurance and types of contracts, inclusion of costs, sufficient premium, sufficient actuarial reserves, business plan, profit and contribution formula, profit sharing. (II) Introduction to pension insurance: Model (states and state changes), present values and reserves, methods for financing them. (III) Pension funds. (IV) Introduction to health insurance mathematics (according to life insurance mathematics): claims amount per risk and profiles, reserves, expense loading, conversion of a contract. (V) Unit-linked life insurance contracts: Short introduction to financial mathematics, pricing of unit-linked contracts (under the risk-neutral measure in the Black-Scholes model), Thiele's differential equation for reserves. Stochastic Interest: no principle of diversification.
- Wolfsdorf: Versicherungsmathematik, Teil 1: Personenversicherung, Teubner, 1997.
- Metzger: Mathematik der Krankenversicherung, Vorlesungsskriptum, 2004.
- Koller: Stochastische Modelle in der Lebensversicherung, Springer, 2000.
Ergänzend:
- Gerber: Life insurance mathematics, Springer, 1997.
- Kainhofer: Einführung in die Finanzmathematik: Diskrete Modelle, Vorlesungsskriptum, TU Wien, 2007.
- Hamke, Rückert: Hedging von fondsgebundneen Lebensversicherungen, Seminararbeit an der Universität Ulm, 2007.
- Kiesel: Financial Methods in Insurance, Course notes, University of Ulm, 2006.
