Moodle

This course provides an introduction to life insurance mathematics broadly conceived, covering insurances against all life-contingent risks, with a particular emphasis on the regulatory framework in Germany. Topics include:

• Multiple-decrement models and actuarial calculation bases
• Expected present values of payment streams (for premiums and benefits)
• Equivalence principle and actuarial reserves
• Applications: whole life insurance, annuities, pensions, private health insurance

The focus of the course is on studying the convergence behavior of local averaging methods (e.g. kernel estimates and nearest neighbor estimates) and of empirical risk minimization. These methods are widely used for solving regression problems and in pattern recognition.

Topics:

• Introduction to the regression problem and to pattern recognition
• Local averaging methods (e.g., kernel smoothing, k-nearest neighbor)
• Concentration inequalities (Hoeffding, Bernstein)
• Sample splitting
• Empirical risk minimization
• Vapnik-Chervonenkis inequality
• Combinatorial aspects of the Vapnik-Chervonenkis theory

Recommended prerequisites: Basic knowledge of modern probability theory (at the level of the mathematics course Stochastik I).