Optimal control of excess-of-loss reinsurance and investment for insurers under a CEV model

The optimal excess-of-loss reinsurance and investment strategies under a constant elasticity of variance (CEV) model for an insurer are considered in this paper. Assume that the insurer’s surplus process is approximated by a Brownian motion with drift, the insurer can purchase excess-of-loss reinsurance and invest his (or her) surplus in a financial market consisting of one risk-free asset and one risky asset whose price is modeled by a CEV model, and the objective of the insurer is to maximize the expected exponential utility from terminal wealth. Two problems are studied, one being a reinsurance-investment problem and the other being an investment-only problem. Explicit expressions for optimal strategies and optimal value functions of the two problems are derived by stochastic control approach and variable change technique. Moreover, several interesting results are found, and some sensitivity analysis and numerical simulations are provided to illustrate our results.