广东工业大学学报 ›› 2022, Vol. 39 ›› Issue (06): 26-35.doi: 10.12052/gdutxb.220043

• 综合研究 • 上一篇    下一篇

暧昧厌恶下含衍生品交易的最优投资与再保险策略

朱怀念, 黄思涵, 黄佳怡, 黄永豪   

  1. 广东工业大学 经济学院, 广东 广州, 510520
  • 收稿日期:2022-03-11 出版日期:2022-11-10 发布日期:2022-11-25
  • 作者简介:朱怀念(1985-) ，男，副教授，博士，硕士生导师，主要研究方向为动态博弈理论及应用、保险精算等，E-mail：zhuhuainian@gdut.edu.cn
  • 基金资助:
    广东省自然科学基金资助项目(2018A030313687)；广东工业大学大学生创新训练计划项目(xj2022118450913)

Ambiguity Aversion and Optimal Investment and Reinsurance Strategies for Insurers with Derivative Trading

Zhu Huai-nian, Huang Si-han, Huang Jia-yi, Huang Yong-hao   

  1. School of Economics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2022-03-11 Online:2022-11-10 Published:2022-11-25

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摘要： 在允许保险资金投资金融衍生品的情境下，如何通过投资与再保险进行风险管控是保险公司亟需解决的问题之一。假设保险公司决策者具有暧昧厌恶偏好，他们对交易市场中的模型参数存在暧昧性，并旨在寻找鲁棒最优投资与再保险策略。暧昧厌恶型的保险公司一方面允许购买比例再保险来控制索赔风险，另一方面通过在包含衍生品的金融市场中投资来实现财富的保值增值。本文以终端财富期望效用最大化为目标构建了鲁棒优化模型，利用动态规划方法给出了优化问题对应的HJB（Hamilton-Jacobi-Bellman）方程，并通过求解HJB方程得到了最大化指数效用的鲁棒最优投资与再保险策略；最后通过数值示例展示了模型相关参数变动对最优投资与再保险策略的影响。研究表明：考虑模型参数的暧昧性及参与衍生品交易可以显著提高保险公司的效用水平。

关键词: 投资与再保险, 暧昧厌恶, 衍生品, Hamilton-Jacobi-Bellman方程

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

中图分类号: 

  • F830.59
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