均值方差保费原理下带有时滞的鲁棒最优再保险和投资策略  

Robust Optimal Reinsurance and Investment Strategy with Delay under Mean-variance Premium Principle

作　　者：胡景铭 刘伟[1] 阎方 胡亦钧[2] HU Jingming;LIU Wei;YAN Fang;HU Yijun(College of Mathematics and System Science,Xinjiang University,Urumqi 830046;School of Mathematics and Statistics,Wuhan University,Wuhan 430072)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046 [2]武汉大学数学与统计学院,武汉430072

出　　处：《工程数学学报》2024年第1期1-16,共16页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11961064,71102118)。

摘　　要：研究带有时滞的保险公司鲁棒最优再保险和投资策略问题。假定保险公司通过购买比例再保险来转移部分索赔风险,且依据广义均值方差保费原理支付再保险保费。同时,保险公司将资产投资于由一种无风险资产和一种风险资产组成的金融市场。风险资产模型的瞬时期望收益率服从均值回复Ornstein-Uhlenbeck(O-U)过程。以保险公司终端财富的指数效用期望最大为优化目标,运用动态规划原理,通过求解相应的Hamilton-Jacobi-Bellman(HJB)方程,得到最优再保险–投资策略以及相应值函数的显式表达式。最后,通过数值分析讨论模型主要参数对最优策略的影响。结果显示,再保险策略主要受保险市场模型参数和无风险资产模型参数的影响,而与风险资产模型的参数及风险资产预期收益率模型的参数无关。另一方面,时滞效应和鲁棒因素会对最优再保险–投资策略产生较大的影响,考虑时滞效应可以增强保险公司财富的稳定性,考虑模型不确定性能有效降低概率测度不精确带来的风险。The problem of robust optimal reinsurance and investment strategies for insur-ance companies with time delay are investigated.By purchasing proportional reinsurance,insurance companies can transfer a portion of their claim risks and pay reinsurance premiums based on the general mean-variance premium principle.At the same time,insurance compa-nies invest their assets in a financial market consisting of a risk-free asset and a risky asset.Assume that the instantaneous expected return rate of the risky asset follows a mean-reverting Ornstein-Uhlenbeck(O-U)process.To maximize the exponential utility expectation of the in-surance company’s terminal wealth,dynamic programming principles are applied.By solving the Hamilton-Jacobi-Bellman(HJB)equation,the optimal reinsurance-investment strategy and the corresponding explicit expression of the value function are obtained.Furthermore,numer-ical analysis shows the impact of the main parameters on the optimal strategy.The results reveal that reinsurance strategy is mainly affected by the parameters of the insurance market and risk-free asset models,rather than the risky asset model or expected return rate.Time delay and robustness factors have a significant impact on the optimal reinsurance-investment strategy.Considering time delay improves the stability of the company’s wealth while incorpo-rating model uncertainty reduces the risk from inaccurate probability measures.

关 键 词：随机最优控制 鲁棒 时滞 再保险–投资策略 均值方差保费原理 

分 类 号：F840[经济管理—保险] O211[理学—概率论与数理统计]