Robust optimal portfolio and proportional reinsurance for an insurer under a CEV model

We investigate a robust optimal portfolio and reinsurance problem under a Cramér-Lundberg risk model for an ambiguity-averse insurer (AAI), who worries about uncertainty in model parameters. Assume that the AAI is allowed to purchase proportional 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 constant elasticity of variance (CEV) model. Using techniques of stochastic control, we first derive the closed-form expressions of the optimal strategies and the corresponding value functions for exponential utility function both in the classic compound Poisson risk process and its diffusion approximation, and then the verification theorem is given. Finally, we present numerical examples to illustrate the effects of model parameters on the optimal investment and reinsurance strategies.