Optimal investment and reinsurance problem with jump-diffusion model

Abstract

In this paper, the optimal investment and reinsurance problem is investigated for a class of the jump-diffusion risk model. Here, the insurer can purchase excess-of-loss reinsurance and invest his or her surplus into a financial market consisting of one risk-free asset and one risk asset whose price is modeled by constant elasticity of variance (CEV) model, the net profit condition and the criterion of maximizing the expected exponential utility of terminal wealth are considered in the CEV financial market. By using stochastic control theory to solve the Hamilton-Jacobi-Bellman (HJB) equation, and the explicit form of the optimal policies and value functions can be obtained. Finally, numerical examples are presented to show the impacts of model parameters on the optimal strategies.

Keywords:

• Excess-of-loss reinsurance
• investment
• constant elasticity of variance (CEV) model
• net profit
• Hamilton-Jacobi-Bellman (HJB) equation

Additional information

Funding

This work was supported in part by the National Nature Science Foundations of China under Grant No. 61673103, 61403248 and the Shanghai Yangfan Program of China under Grant 14YF1409800.