The paper studies an optimal investment and reinsurance problem for an ambiguity-averse insurer (AAI) who aims to minimize the ruin probability under model ambiguity. The insurer is allowed to purchase a proportional reinsurance and invest in one risky asset. The surplus process of the insurer is described by a diffusion risk model and the price process of risky asset is described by the constant elasticity variance (CEV) model. According to the dynamic programming principle, the paper derives the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The optimal strategy and value function are obtained explicitly for special elasticity coefficients. Finally, numerical models illustrate the effects of model parameters on optimal strategy and value function. The paper finds that, the investment and reinsurance strategy of the insurer becomes more conservative when the insurer is more ambiguity averse.
