模糊厌恶下考虑巨灾债券发行的最优投资与风险管理策略

摘要/Abstract

摘要：

气候与环境的变化加剧了自然灾害的频发态势, 对保险公司的风险管理造成了严峻挑战. 因此, 探究保险公司在面临自然灾害等巨灾风险时的最优投资与再保险策略极其必要. 论文创新性地融合了巨灾债券发行和模型不确定性两个因素到传统的最优投资-再保险策略研究中. 通过运用随机控制理论和动态规划方法, 得出了最优投资-再保-巨灾债券发行策略的解析解. 通过数值模拟, 揭示了保险公司发行巨灾债券后最优投资-再保险策略的动态变化特征. 同时, 探讨了市场相关性、模糊厌恶系数等关键参数对策略选择的敏感性和经济影响. 研究结果表明, 巨灾债券发行 (购买) 可以有效替代再保险, 发行 (购买) 量增加时, 再保险购买减少; 巨债券和保险市场相关性的增强可以促使保险公司减少风险投资、增加巨灾债券持有; 不确定性环境下, 保险公司将更加依赖巨灾债券进行风险管理, 并倾向于投资确定性高的市场; 同时随着资金增加, 投资策略趋于保守.

关键词: 模糊, 巨灾债券, 最优策略, 破产概率.

Abstract:

The frequency of natural disasters, exacerbated by climate and environmental changes, poses severe challenges to insurance companies' risk management. Therefore, it is crucial to explore optimal investment and reinsurance strategies for insurance companies when facing catastrophic risks such as natural disasters. This paper innovatively integrates two factors, catastrophe bond issuance and model uncertainty, into traditional research on optimal investment-reinsurance strategies. By employing stochastic control theory and dynamic programming methods, the paper derives analytical solutions for optimal investment-reinsurance-catastrophe bond issuance strategies. Through numerical simulation analysis, it reveals the dynamic characteristics of optimal investment-reinsurance strategies after insurance companies issue catastrophe bonds. Simultaneously, it discusses the sensitivity and economic impact of key parameters such as market correlation and ambiguity aversion coefficients on strategy selection. The research results indicate that catastrophe bond issuance/purchase can effectively substitute for reinsurance, with a decrease in reinsurance purchases as the issuance/purchase volume increases. Enhanced correlation between catastrophe bonds and the insurance market prompts insurance companies to reduce venture investments and increase catastrophe bond holdings. In uncertain environments, insurance companies rely more on catastrophe bonds for risk management and tend to invest in markets with high certainty. Additionally, as capital increases, investment strategies become more conservative.

Key words: ambiguity, CAT bonds, optimal strategies, ruin probability.

中图分类号:

刘兵, 钱通, 李鹏. 模糊厌恶下考虑巨灾债券发行的最优投资与风险管理策略[J]. 数学物理学报, 2026, 46(3): 1255-1269.

Bing Liu, Tong Qian, Peng Li. Optimal Investment and Risk Management Strategies Considering Catastrophe Bond Issuance Under Ambiguity Aversion[J]. Acta mathematica scientia,Series A, 2026, 46(3): 1255-1269.

图/表 5

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