时滞效应下多保险公司竞争的最优策略

Optimal Strategies for Multi-Insurance Company Competition under Time-Delay Effects

摘要: 保险是一种风险管理工具，通过支付保费，个人或企业可以将潜在的经济损失转移给保险公司。再保险则是保险公司为了分散自身风险而采取的一种策略。保险公司将其承保的部分风险转移给再保险公司，以减轻自身在重大损失事件中的财务压力。保险和再保险共同构成了风险管理的多层次体系，为社会经济的稳定运行提供了重要保障，所以对保险和再保险的研究具有重要的理论和实践意义。本研究聚焦于时滞效应下的最优再保险投资策略问题。研究内容主要为：在期望效用最大化准则下，多保险公司的最优再保险投资问题。首先金融市场由无风险资产和风险资产构成，其中风险资产的表达式服从Heston模型，并在时滞效应的框架下推导出保险公司的财富过程，随后针对n家保险公司参与的竞争模型，通过运用动态规划原理和随机最优控制理论，分别求解了n家保险公司的最优投资策略和最优再保险策略的解析解。

Abstract: Insurance is a risk management tool that allows individuals or businesses to pass on potential financial losses to insurance companies by paying premiums. Reinsurance is a strategy adopted by insurance companies to spread their own risks. Insurers transfer some of the risks they cover to reinsurers to relieve their own financial stress in the event of a major loss. Insurance and reinsurance together constitute a multi-level system of risk management, which provides an important guarantee for the stable operation of social economy, so the study of insurance and reinsurance has important theoretical and practical significance. This study focuses on the optimal reinsurance investment strategy under the time-lag effect. The research content mainly includes the optimal reinsurance-investment problem for multiple insurance companies under the expected utility maximization criterion. Firstly, the financial market consists of a risk-free asset and a risky asset, where the dynamics of the risky asset follow the Heston model. The wealth process of the insurance company is derived under the framework of time-delay effects. Subsequently, for the competitive model involving n insurance companies, the explicit solutions for the optimal investment strategies and optimal reinsurance strategies of the n insurance companies are derived by applying the dynamic programming principle and stochastic optimal control theory.