Optimal investment for an insurer with exponential utility preference

This paper considers the optimal investment choice for a general insurer in the sense of maximizing the exponential utility of his or her reserve at a future time. The claim process is supposed to be a pure jump process (not necessarily compound Poisson) and the insurer has the option of investing in multiple risky assets whose price processes are described by the Black–Scholes market model. It is shown in this paper that the optimal strategy is to put a fixed amount of money in each risky asset if there is no risk-free asset. If there is a risk-free asset, the discounted amount held in each risky asset is fixed. In the case where the claim process is compound Poisson, the optimal strategy with respect to a properly selected utility function can result in a reserve process which is safer than that without risky investment.