A Numerical Study of Reserves and Risk Measures in Life Insurance

Mikkel Dahl, Danemark

In this paper we study different methods for calculating reserves for life insurance contracts with deterministic benefits in a slight simplification of the model in Dahl (2005c). Hence, the model considered includes the equity, standard interest rate and reinvestment risks on the financial side and the systematic and unsystematic mortality risks on the insurance side. We consider market reserves calculated by the no arbitrage principle, only. Further- more, we consider the following alternative approaches to pricing the dependence on the reinvestment risk: super-replication and the principles of a level long term yield/forward rate curve. Combined with the no arbitrage principle for the remaining risks, these principles give reserves, which can be compared to the market reserves. Moreover, the risk measures of Value at Risk and tail conditional expectation are considered. These different reservation principles and the relationship to the risk measures are compared numerically.
Date: 2 June - Time: 8:30 to 10:00 - Room: 251
Theme: 1.B. Solvency measurements and asset-liability management