一类随机模型下最优再保险投资策略
Optimal Reinsurance-Investment Strategies under a Stochastic Model
摘要: 本文研究了一类最优再保险–投资问题，其中保险公司的盈余过程遵循带漂移的布朗运动。本文所研究的模型允许保险公司通过购买比例再保险来分担公司风险，并将财富投资于金融市场。金融市场由一种无风险资产和一种有风险资产组成，其中风险的市场价格由马尔可夫仿射平方根模型描述。文章应用随机最优控制理论得到了幂效用下最优再保险–投资策略的显示解，并给出数值算例分析了主要模型参数对最优再保险–投资策略的影响。
Abstract: This paper studies an optimal reinsurance-investment problem in which the insurance company’s surplus process follows Brownian motion with drift. The model studied in this paper allows in-surance companies to share corporate risks by purchasing proportional reinsurance and invest their wealth in financial markets. The financial market consists of a risk-free asset and a risky asset, in which the market price of the risk is described by the Markov affine-form square root model. In this paper, the explicit solution of optimal reinsurance and investment strategy under power utility is obtained by using stochastic optimal control theory, and numerical examples are given to analyze the influence of main model parameters on optimal reinsurance and investment strategy.
文章引用：黄文锐, 蔡晓霞. 一类随机模型下最优再保险投资策略[J]. 理论数学, 2023, 13(3): 541-554. https://doi.org/10.12677/PM.2023.133058

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