Loss Analysis of a Life Insurance Company Applying Discrete-time Risk-minimizing Hedging Strategies

In this paper, we consider the net loss of a life insurance company issuing identical equity-linked pure endowment contracts in the case of periodic premiums. Under this construction, financial risks as well as the mortality risk are included. Based on Møller (1998), we particularly investigate the situation where the company applies a time-discretized risk-minimizing hedging strategy, i.e., a trading restriction is imposed on a continuous-time risk-minimizing strategy. Therefore, the considered model is incomplete where the incompleteness results not only from the mortality risk but also from the trading restrictions. Through an illustrative example, it is observed from the simulations that a substantial reduction in the ruin probability is achieved by using the time-discretized risk-minimizing strategy. However, as the hedging frequency is set higher, this advantage almost disappears, because a higher frequency leads to more hedging errors which constitute a vital part of the hedger’s net loss. In order to improve the simulated results, another type of discrete-time risk-minimizing strategy is taken into consideration. It is obtained by discretizing the hedging model instead of the hedging strategy. For this purpose, Møller’s (2001) discrete-time (binomial) risk-minimizing strategy is adopted. For both strategies, a number of sensitivity analyses are carried out, e.g. how the ruin probability changes with the fair combination of the minimum interest rate guarantee and the participation rate.