Optimal Investment-reinsurance Strategies for an Insurer with Options Trading Under Model Ambiguity

This paper investigates the optimal investment-reinsurance problems for an ambiguity averse insurer with access to the options market, who worries about ambiguity and aims to find robust strategies to minimize the probability of ruin. The insurer is allowed to invest in the financial market, which consists of a risk-free asset and a risky asset, and purchase an option on another risky asset to hedge its risk. In addition, the insurer can purchase proportional reinsurance to transfer part of its claim risk. By applying dynamic programming principle, we obtain closed-form solutions for the corresponding optimal investment-reinsurance strategies and the value functions. We elucidate how investment options improve the insurer's portfolio performance and find that the change in the correlation coefficient between the financial market and the options market can significantly affect the insurer's optimal investment-reinsurance strategy. We also compare the effects of different ambiguity aversion coefficients in the markets and provide some numerical examples and economic explanations to illustrate our results.