The optimal investment-reinsurance strategies for ambiguity aversion insurer in uncertain environment

Abstract

<p style='text-indent:20px;'>We study the optimal investment-reinsurance strategies for insurer, who is assumed to be ambiguous about factors related to the stock process and surplus process. In the financial market, the stock and derivatives are traded freely, the optimal investment-reinsurance strategies are obtained under the worst-case scenario with or without derivative trading. We find the evidence that the optimal exposures to different risks of the stock are significantly affected by the ambiguity aversion to the corresponding risk factors. Insurer who ignores model uncertainty always incur welfare losses, which can be proved to be strictly positive. Furthermore, we find that volatility ambiguity has a smaller impact in incomplete markets and surplus process ambiguity has a great impact on reinsurance strategies. Numerical experiments are provided to demonstrate the impact of the optimal exposure and utility loss with different parameters.</p>