Profit sharing: a stochastic control approach
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A majority of life insurance contracts encompasses a guaranteed interest rate and a participation to earnings of the insurance company. This participation, called profit share, is usually commuted into an increase of benefits. Furthermore, the amount distributed as a profit share is freely chosen by insurers in most of European countries. The insurer's decision to grant a profit share or not is in this context, influenced by the competition on the market and by shareholders' waitings. This paper proposes a method adapted to this situation, to optimize both the profit shares distribution and the asset allocation, based upon a stochastic control approach. In this setting, optimal strategies are those maximizing the expected economic utilities of future profit shares and of the insurer's future economic wealth.