Abstract
This paper discusses the optimal problems of reinsurance and investment for insurance companies with fractional power utility function. Insurance companies can buy reinsurance contracts and invest their wealth in risk-free or risk-free financial securities. It is assumed that the insurance company surplus process is estimated using Brownian motion. The aim of the insurance company is to seek optimal reinsurance and investment strategies by maximizing expected utility expectations from the final wealth. The explicit form for the optimal strategy is determined by the stochastic optimal control theory approach, which uses the Hamilton Jacobi Bellman equations.