Utility maximization and risk minimization in life and pension insurance

摘要

We consider a life insurance company that seeks to optimize the pension benefits on behalf of an insured. We take the uncertain course of life of the insured explicitly into account and thus have a non-standard financial optimization problem for which we propose a two-step approach. First, according to a certain preference structure and under a certain fairness constraint, an optimal pension payment process is obtained. This leaves the company with a non-hedgeable liability, for which we then discuss two quadratic hedging approaches. We obtain general results on dividend optimization, indicating that some widely used strategies are suboptimal, and semi-explicit expressions for the optimal bonus and investment strategies.