模糊厌恶型保险公司最优再保险及最优投资策略 –以中国股票市场为例
Ambiguity Aversion Type Insurance Company’s Optimal Re-insurance and Investment Strategy - Taking the Chinese Stock Market as an Example
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摘要: 近年来, 对保险人最优策略的研究已成为保险精算领域中备受瞩目的经典话题. 以往的 研究多数都是在确定的模型下应用随机分析的方法找到使保险人终端财富期望效用最大化的最优策 略, 对模型不确定情形下保险人最优策略进行分析的文献较少. 因此, 本文从新的视角出发, 假设描绘 金融市场中风险资产价格过程以及保险人索赔过程的模型存在不确定性. 并且保险人对于这种模型不 确定性持有厌恶态度, 通过求解 HJB 方程最终得到了模糊厌恶型保险人最优再保险及最优投资策略的 解析解. 同时, 我们应用真实市场中的数据对模型中的部分参数进行了估计, 并进行了数值分析.Abstract: The optimal reinsurance and investment strategy for insurers has always been a topic worthy of in-depth exploration. However, constrained by actuarial techniques and the uncertainty of financial markets, the ambiguity of insurers’ model estimates for financial markets and claims processes should not be overlooked. This paper assumes that insurers exhibit ambiguity aversion to financial markets and claims processes. Insurers, in the course of their operations, can purchase reinsurance to diversify risks and invest in risk assets and risk-free assets in the financial market to generate returns. The price process of risk assets follows the CEV model. Under these conditions, the paper provides analytical solutions for the insurer’s optimal investment strategy and optimal reinsurance to maximize the insurer’s terminal wealth utility objective. Additionally, the study incorporates parameter estimation from the Chinese stock market for numerical analysis.