Optimal Layer Reinsurance And Investment For The Diffusion Approximation Risk Model With Common Shock Dependence

In this paper, we study the optimal layer reinsurance and investment with com-mon shock dependence to maximize the expected exponential utility from terminal wealth. It is assumed that the claim sizes are approximated by a diffusion process and the financial market the insurer invested in consists of a risk-free asset and one risky asset. When the risk assets are independent with claim sizes, we prove that the optimal layer reinsurance is the pure excess of loss reinsurance under the expected value principle. At the same time, by the technique of stochastic control theory and Hamilton-Jacobi-Bellman equation, we derive the closed-form solution and prove that the optimal solution is unique. Combining the boundary condition and the optimal s-trategies, we obtain the corresponding value function. Whereas, when the risky assets and claim sizes are not independent, we consider the effect from their correlation coef-ficient on our optimal strategies and the relationship between the optimal reinsurance variables. At last, we also try to show the impact of time, the intensity of the Pois-son processes and even the safety loading of reinsurance on the optimal reinsurance strategies by some numerical examples.