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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 ›› 2022, Vol. 39 ›› Issue (1): 1-19.doi: 10.3969/j.issn.1005-3085.2022.01.001

• •    下一篇

基于模型不确定性的保险人最优投资再保险问题研究

王雨薇,   荣喜民,   赵  慧   

  1. 天津大学数学学院，天津 300350
  • 出版日期:2022-02-15 发布日期:2022-04-15
  • 基金资助:
    国家自然科学基金 (11771329; 11871052).

Optimal Reinsurance and Investment Strategies for Insurers with Ambiguity Aversion: Minimizing the Probability of Ruin

WANG Yuwei,   RONG Ximin,   ZHAO Hui   

  1. School of Mathematics, Tianjin University, Tianjin 300350
  • Online:2022-02-15 Published:2022-04-15
  • Supported by:
    The National Natural Science Foundation of China (11771329; 11871052).

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61

摘要：

研究了以破产概率最小化为目标的模糊厌恶型保险人的最优投资再保险问题。假设保险人可购买比例再保险，同时可投资于一个风险资产。保险人的盈余过程由扩散风险模型描述，风险资产的价格过程由常方差弹性 (CEV) 模型描述。根据动态规划原理建立了优化问题相应的 HJB 方程，针对特殊的弹性系数给出了保险人的最优鲁棒投资再保险策略的解析解。最后，通过数值模型分析了模型参数对最优投资-比例再保险策略和值函数的影响。研究发现保险人的模糊厌恶程度越高，其采取的投资再保险策略呈现出越保守的特点。

关键词: 破产概率, 模型不确定, 投资策略, 再保险策略, HJB 方程, 随机最优控制

Abstract:

The paper studies an optimal investment and reinsurance problem for an ambiguity-averse insurer (AAI) who aims to minimize the ruin probability under model ambiguity. The insurer is allowed to purchase a proportional reinsurance and invest in one risky asset. The surplus process of the insurer is described by a diffusion risk model and the price process of risky asset is described by the constant elasticity variance (CEV) model. According to the dynamic programming principle, the paper derives the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The optimal strategy and value function are obtained explicitly for special elasticity coefficients. Finally, numerical models illustrate the effects of model parameters on optimal strategy and value function. The paper finds that, the investment and reinsurance strategy of the insurer becomes more conservative when the insurer is more ambiguity averse.

Key words: ruin probability, model ambiguity, investment strategy, reinsurance strategy, HJB equation, stochastic optimal control

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