On Optimal Proportional Reinsurance Of The Compound Poisson Model Perturbed By Diffusion

In this paper, we mainly study the optimal proportional reinsurance of the Compound Poisson model perturbed by diffusion which is a further expansion of the Compound Poisson model.In this model,proportional reinsurance is allowed in order to decrease the ultimate ruin probability.Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal strategy and develop a numerical procedure to solve the HJB equation.Then we prove a verification theorem in order to show that the solution of the HJB equation solves the optimisation problem.The solution exists and is unique.This paper includes four chapters. The first chapter is the introduction. In the second chapter, the Compound Poisson model perturbed by diffusion and the problem of optimal reinsurance are introduced. The HJB equation approach is embodied in the third chapter-the main body of this paper, and then we solve the equation. The last chapter gives an example.