• • 上一篇    

具有索赔相依的最优再保险与投资策略

杨鹏   

  1. 西安财经大学统计学院, 西安 710100
  • 收稿日期:2021-10-25 修回日期:2022-03-06 发布日期:2022-07-29
  • 基金资助:
    教育部人文社会科学研究西部项目-青年基金(21XJC910001)资助课题.

杨鹏. 具有索赔相依的最优再保险与投资策略[J]. 系统科学与数学, 2022, 42(6): 1566-1579.

YANG Peng. Optimal Reinsurance and Investment Strategies with Claim Dependence[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(6): 1566-1579.

Optimal Reinsurance and Investment Strategies with Claim Dependence

YANG Peng   

  1. School of Statistics, Xi'an University of Finance and Economics, Xi'an 710100
  • Received:2021-10-25 Revised:2022-03-06 Published:2022-07-29
大量实证研究表明,未来索赔与历史索赔相关.基于外推偏差法,文章建立了未来索赔对历史索赔的相依性,给出了保费计算方式,进而建立了保险公司的盈余过程.为了规避索赔风险,考虑了再保险;为了增加财富,考虑了在金融市场投资.因此,保险公司的最优决策包含再保险的最优决策和投资的最优决策.利用随机控制理论建立了值函数满足的Hamilton-Jacobi-Bellman (HJB)方程和验证定理.进而,在期望效用框架下,导出了最优再保险和投资策略.同时得到了保险公司集中化和分散化的投资准则.最终,在理论和数值实验两方面详细分析了模型关键参数对最优再保险和投资策略的影响,得到了一些深刻的决策建议.
A large number of empirical studies have shown that future claims are correlated with historical claims. Based on the extrapolation method, this paper establishes the dependence of future claims on historical claims, presents the premium calculation method, and then establishes the surplus process of insurance company. In order to avoid the claim risks, reinsurance is considered; in order to increase wealth, investment in financial market is considered. Therefore, the optimal decision-marking of the insurance company includes the optimal decision-marking of reinsurance and the optimal decision-marking of investment. We establish the Hamilton-Jacobi-Bellman (HJB) equation of the value function and verification theorem by using stochastic control theory. Then, under the expected utility framework, the optimal reinsurance and investment strategies are derived. Meanwhile, the investment criteria of centralization and decentralization of the insurance company are obtained. Finally, the influence of the key parameters of the model on the optimal reinsurance and investment strategy is analyzed in detail in both theoretical and numerical experiments, and some profound decision-making suggestions are obtained.

MR(2010)主题分类: 

()
[1] Niehaus G, Terry A.Evidence on the time series properties of insurance premiums and causes of the underwriting cycle:New support for the capital market imperfection hypothesis.Journal of Risk and Insurance, 1993, 60(3):466-479.
[2] Browne M J, Hoyt R E.The demand for flood insurance:Empirical evidence.Journal of Risk and Uncertainty, 2000, 20(3):291-306.
[3] Ranyard R, McHugh S.Defusing the risk of borrowing:The psychology of payment protection insurance decisions.Journal of Economic Psychology, 2012, 33(4):738-748.
[4] Barberis N, Greenwood R, Jin L, et al.X-CAPM:An extrapolative capital asset pricing model.Journal of Financial Economics, 2015, 115(1):1-24.
[5] Chen S, Hu D, Wang H.Optimal reinsurance problem with extrapolative claim expectation.Optimal Control Applications and Methods, 2018, 39(1):78-94.
[6] Hu D, Wang H.Optimal proportional reinsurance with a loss-dependent premium principle.Scandinavian Actuarial Journal, 2019, 2019(9):752-767.
[7] Grandell J.Aspects of Risk Theory.Springer-Verlag, New York, 1991.
[8] Watt R, Vazquez F J.Full insurance, Bayesian updated premiums, and adverse selection.Geneva Papers on Risk and Insurance Theory, 1997, 22(2):135-150.
[9] Fung H G, Lai G C, Patterson G A, et al.Underwriting cycles in property and liability insurance:An empirical analysis of industry and by line data.Journal of Risk and Insurance, 1998, 65(4):539-561.
[10] Merton R C.On estimating the expected return on the market:An exploratory investigation.Journal of Financial Economics, 1980, 8(4):323-361.
[11] Basak S.A model of dynamic equilibrium asset pricing with heterogeneous beliefs and extraneous risk.Journal of Economic Dynamics and Control, 2000, 24(1):63-95.
[12] Fleming W H, Soner H M.Controlled Markov Processes and Viscosity Solutions.Berlin-New York:Springer, 1993.
[13] Brachetta M, Ceci C.Optimal proportional reinsurance and investment for stochastic factor models.Insurance:Mathematics and Economics, 2019, 87:15-33.
[1] 唐旻, 黄志刚. 引入投资者关注度的股指收益率预测研究——基于差分进化算法极限学习机模型[J]. 系统科学与数学, 2022, 42(6): 1503-1518.
[2] 赵霞, 时雨, 欧阳资生. 基于尾部风险差异性态度的多目标投资组合策略[J]. 系统科学与数学, 2022, 42(5): 1129-1144.
[3] 孙会霞, 赵慧敏, 张超, 郑田田. 基于集成学习的加权投资组合优化[J]. 系统科学与数学, 2022, 42(5): 1145-1160.
[4] 钱龙, 韦江, 赵慧敏, 倪宣明. 基于AdaBoost的投资组合优化[J]. 系统科学与数学, 2022, 42(2): 271-286.
[5] 董迎辉, 魏思媛, 殷子涵. 投资策略和VaR约束下基于相对业绩的最优资产配置[J]. 系统科学与数学, 2021, 41(9): 2505-2519.
[6] 王佩, 张玲, 范思雨. 股票误价和信息部分可观测下的时间一致再保险和投资策略[J]. 系统科学与数学, 2021, 41(7): 1834-1855.
[7] 史爱玲, 李仲飞. 带遗产动机和最低业绩需求的DC 型养老金的优化投资问题[J]. 系统科学与数学, 2021, 41(7): 1905-1926.
[8] 王盼盼. 石油金融化、投资者预期与``石油-美元''机制的结构变动 ------基于原油双重属性视角的研究[J]. 系统科学与数学, 2021, 41(6): 1585-1609.
[9] 李文辉, 王竟竟. 基于不同规模指数的中国股票市场周内效应异质性[J]. 系统科学与数学, 2021, 41(6): 1682-1692.
[10] 崔金鑫, 邹辉文. 国际股市间动态相依性及高阶矩风险溢出效应研究[J]. 系统科学与数学, 2021, 41(4): 976-1006.
[11] 侯胜杰, 关忠诚, 董雪璠. 基于熵和CVaR的多目标投资组合模型及实证研究[J]. 系统科学与数学, 2021, 41(3): 640-652.
[12] 孙会霞,倪宣明,钱龙,赵慧敏. 基于长期CVaR约束的高频投资组合优化[J]. 系统科学与数学, 2021, 41(2): 344-360.
[13] 李铮,熊熊,牟擎天,周炜星. 基于对数周期幂律奇异性模型的资产价格泡沫预测[J]. 系统科学与数学, 2021, 41(2): 361-372.
[14] 杨鹏,杨志江. 相对表现视角下的再保险与投资策略[J]. 系统科学与数学, 2021, 41(2): 517-532.
[15] 蔡毅, 唐振鹏, 吴俊传, 张婷婷, 杜晓旭, 陈凯杰. 异质投资者情绪对股市的影响研究------基于文本语义分析[J]. 系统科学与数学, 2021, 41(11): 3093-3108.
阅读次数
全文


摘要