暧昧厌恶下含衍生品交易的最优投资与再保险策略

doi:10.12052/gdutxb.220043

Abstract

Abstract: Assume that the investment portfolio includes an derivative，we study the optimal investment and proportional reinsurance strategies for ambiguity averse insurers, who are concerned about the potential model ambiguity and aim to seek the robust optimal investment and reinsurance strategies. The ambiguity-averse insurers are allowed to purchase reinsurance treaty to mitigate individual claim risks; and can invest in a financial market consisting of one risk-free asset, one risky stock and one derivative. The ambiguity-averse insurers assumed to have exponential utility, and we formulate the optimization problem as an utility maximization problem. By applying the dynamic programming approach, we derive the HJB equation for the value function. Meanwhile, we obtain the closed-form solutions to the optimal investment and reinsurance strategies. Finally, we provide some numerical simulations together with sound economic implications. More important, we demonstrate the utility improvement when considering derivative trading and parameter ambiguity, and find that derivative trading can significantly improve utility when return volatility increases.

Key words: investment and reinsurance, ambiguity aversion, derivative, Hamilton-Jacobi-Bellman equation

CLC Number:

F830.59

Zhu Huai-nian, Huang Si-han, Huang Jia-yi, Huang Yong-hao. Ambiguity Aversion and Optimal Investment and Reinsurance Strategies for Insurers with Derivative Trading[J].Journal of Guangdong University of Technology, 2022, 39(06): 26-35.

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