Optimal Investment and Optimal Reinsurance

Yuedi Liu

In this paper, Aiming at the delay claim risk model, the optimal investment and optimal reinsurance strategy which makes the expected index utility maximum of the final wealth are studied under the principle of variance premium principle. Firstly, when the optimal reinsurance is in the form of proportional reinsurance, we use diffusion approximation to approximate the claim process of insurance companies. then, we use the dynamic programming principle to solve the Hamilton-Jacobi-Bellman equation. Finally, we obtain the explicit optimal strategy and the value function.