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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (2): 245-265.doi: 10.3969/j.issn.1005-3085.2024.02.004

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相依风险模型下保险公司和再保险公司的鲁棒最优再保险和投资策略

慕  蕊1,  马世霞2,  张欣茹2   

  1. 1. 山东华宇工学院经济管理学院，德州 253000
    2. 河北工业大学理学院，天津 300401
  • 收稿日期:2021-07-06 接受日期:2022-08-12 出版日期:2024-04-15 发布日期:2024-06-15
  • 基金资助:
    国家自然科学基金 (12071107)；2023 年度智慧物流与供应链研究中心阶段研究成果 (2023HYWL09).

Robust Optimal Reinsurance and Investment Strategies for the Insurer and the Reinsurer under Dependent Risk Model

MU Rui1,  MA Shixia2,  ZHANG Xinru2   

  1. 1. School of Economics and Management, Shandong Huayu University of Technology, Dezhou 253000;
    2. School of Science, Hebei University of Technology, Tianjin 300401
  • Received:2021-07-06 Accepted:2022-08-12 Online:2024-04-15 Published:2024-06-15
  • Supported by:
    The National Natural Science Foundation of China (12071107); the Research Achievements of 2023 Smart Logistics and Supply Chain Research Center (2023HYWL09).

摘要：

在具有共同冲击相依风险模型下，研究了保险公司和再保险公司共同利益的最优再保险和投资问题。假设保险公司和再保险公司的盈余过程由扩散逼近模型来刻画，并且保险公司可以购买比例再保险来分散风险，再保险保费由均值方差保费原则计算。同时，保险公司和再保险公司都可投资于无风险资产和风险资产，其中风险资产的价格过程遵循平方根因子过程，在使保险公司和再保险公司终端财富加权和的期望指数效用最大化的条件下，应用随机控制理论，建立了鲁棒 Hamilton-Jacobi-Bellman (HJB) 方程并且得到了最优再保险和投资策略以及相应的值函数。此外，通过一些数值例子来说明某些模型参数对最优再保险和投资策略的影响。

关键词: 相依风险, 共同利益, 期望–方差保费原则, 模糊厌恶, 平方根因子过程

Abstract:

This paper studies the optimal reinsurance and investment problem with consideration of joint interests of an insurer and a reinsurer under the risk model with common shock dependence. Suppose that the surplus process of the insurance company and the reinsurance company is described by the diffusion approximation model, and the insurance company can purchase proportional reinsurance whose reinsurance premium is calculated by the mean-variance premium principle to disperse risks. Both insurance companies and reinsurance companies can invest in risk-free assets and risk assets whose price process follows the square-root factor process. By stochastic control theory, we establish the robust Hamilton-Jacobi-Bellman (HJB) equation and obtain the optimal reinsurance-investment strategies and the corresponding value functions under the objective of maximizing the expected utility of the weighted sum of terminal wealth of insurance companies and reinsurance companies. In addition, we give some numerical examples to illustrate the effects of some model parameters on the optimal reinsurance and investment strategies.

Key words: dependent risk, common interest, mean-variance premium principle, ambiguity averse, square-root factor process

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