跳扩散模型下稳健最优再保险和CDS投资策略
Robust Optimal Proportional Reinsurance and CDS Investment Strategies for Insurer with Jump-Diffusion Risk
摘要:
本文研究了跳扩散风险模型下，具有模糊厌恶的保险公司的最优投资与再保险策略问题。假设保险公司可以购买比例再保险，也可以投资于一个无风险资产、一个风险资产和一种信用违约互换债券构成的金融市场。我们在均值–方差准则下，最大化终端财富的期望。根据扩展的Hamilton-Jacobi-Bellman (HJB)方程，我们求出了违约前和违约后的最优投资与再保险策略。最后，我们给出了一些数值例子验证模型不确定性和信用违约互换债券投资对策略的影响。
Abstract:
This paper considers an optimal reinsurance and investment problem in a model with jump diffusion for an ambiguity averse insurer (AAI). The insurer is allowed to purchase proportional reinsurance and invest in a financial market, which consists of a risk-free asset, a risky asset and a credit default swap (CDS). We maximize the expectation of the terminal wealth under the mean-variance criterion. By solving the corresponding extended Hamilton-Jacobi-Bellman (HJB) equations, the optimal investment-reinsurance strategies and the corresponding equilibrium value functions are obtained for the post-default case and pre-default case. Finally, we provide numerical examples to illustrate the effects of model uncertainty and Credit Default Swap (CDS).
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