CEV模型和违约风险下具有稀疏相依风险的鲁棒最优再保险和投资策略
Robust Optimal Investment and Reinsurance Strategies with Thinning Dependent Risks under CEV Model and Default Risk
摘要: 本文研究了一个具有稀疏相依风险的模糊厌恶保险公司(AAI)的最优再保险和投资问题。AAI通过购买比例再保险来控制保险风险，再保险保费遵循广义期望值–方差原则，并将其财富投资于一个储蓄账户、股票和可违约债券组成的金融市场，其中股票价格过程服从常方差弹性(CEV)模型。以终端财富的期望指数效用最大为目标，利用随机控制方法分别建立了违约后和违约前的鲁棒Hamilton-Jacobi-Bellman (HJB)方程，并分别推导出鲁棒最优再保险和投资策略和相应的值函数。最后，用数值例子分析了模型参数对鲁棒最优策略的影响并给出相应的经济解释。
Abstract: This paper investigates the optimal reinsurance and investment problem with thinning dependent risks for an ambiguity-averse insurer (AAI). It is assumed that AAI manages insurance risk by pur-chasing proportional reinsurance, in which the reinsurance premium is calculated by the general-ized mean-variance premium principle, and its wealth is invested in a financial market consisting of a saving account, a defaultable bond and a stock whose price process obeys the constant elasticity of variance (CEV) model. The AAI aims to maximize the expected exponential utility of terminal wealth. The HJB equation corresponding to the robust optimal problem is established by using stochastic control method, and the robust optimal strategy and value function are obtained for the pre-default and post-default case respectively. Finally, numerical examples are presented to illustrate the ef-fects of parameters on the robust optimal strategies and the corresponding economic explanations are given.
文章引用：张雨萌, 马世霞, 张欣茹. CEV模型和违约风险下具有稀疏相依风险的鲁棒最优再保险和投资策略[J]. 应用数学进展, 2023, 12(3): 1022-1034. https://doi.org/10.12677/AAM.2023.123104

参考文献

[1] Liang, X.Q., Liang, Z.B. and Young, V.R. (2020) Optimal Reinsurance under the Mean-Variance Premium Principle to Minimize the Probability of Ruin. Insurance Mathematics and Economics, 92, 128-146. [Google Scholar] [CrossRef] 
[2] Zhang, Q. and Chen, P. (2019) Robust Optimal Proportional Reinsurance and Investment Strategy for an Insurer with Defaultable Risks and Jumps. Computational and Applied Mathematics, 356, 46-66. [Google Scholar] [CrossRef] 
[3] Zhao, H., Shen, Y. and Zeng, Y. (2016) Time-Consistent Invest-ment-Reinsurance Strategy for Mean-Variance Insurers with a Defaultable Security. Mathematical Analysis and Applica-tions, 437, 1036-1057. [Google Scholar] [CrossRef] 
[4] Liang, Z.B. and Yuen, K.C. (2016) Optimal Dynamic Reinsurance with Dependent Risks: Variance Premium Principle. Scandinavian Actuarial, 1, 18-36. [Google Scholar] [CrossRef] 
[5] Yuen, K.C., Liang, Z.B. and Zhou, M. (2015) Optimal Pro-portional Reinsurance with Common Shock Dependence. Insurance Mathematics and Economics, 64, 1-13. [Google Scholar] [CrossRef] 
[6] Sun, J.Y., Yao, H.X. and Kang, Z.L. (2019) Robust Optimal Reinsurance-Investment Strategies for an Insurer with Multiple Dependent Risks. Insurance Mathematics and Econom-ics, 89, 157-170. [Google Scholar] [CrossRef] 
[7] Zhang, Y. and Zhao, P.B. (2019) Robust Optimal Ex-cess-of-Loss Reinsurance and Investment Problem with Delay and Dependent Risks. Discrete Dynamics in Nature and Society, 21, Article ID: 6805351. [Google Scholar] [CrossRef] 
[8] Wang, G.J. and Yuen, K.C. (2005) On a Correlated Aggregate Claims Model with Thinning-Dependence Structure. Insurance Mathematics and Economics, 36, 456-468. [Google Scholar] [CrossRef] 
[9] Han, X., Liang, Z.B. and Yuen, K.C. (2018) Optimal Pro-portional Reinsurance to Minimize the Probability of Drawdown under Thinning-Dependence Structure. Scandinavian Actuarial, 10, 863-889. [Google Scholar] [CrossRef] 
[10] Zhang, Y., Zhao, P.B. and Kou, B.Y. (2021) Optimal Ex-cess-of-Loss Reinsurance and Investment Problem with Thinning Dependent Risks under Heston Model. Computational and Applied Mathematics, 382, Article ID: 113082. [Google Scholar] [CrossRef] 
[11] Sun, Z.Y., Zheng, X.X. and Zhang, X. (2017) Robust Optimal In-vestment and Reinsurance of an Insurer under Variance Premium Principle and Default Risk. Mathematical Analysis and Applications, 446, 1666-1686. [Google Scholar] [CrossRef] 
[12] Zheng, X.X., Zhou, J.M. and Sun, Z.Y. (2016) Robust Optimal Portfolio and Proportional Reinsurance for an Insurer under a CEV Model. Insurance Mathematics and Economics, 67, 77-87. [Google Scholar] [CrossRef] 
[13] Wang, S.X., Rong, X.M. and Zhao, H. (2019) Optimal Time-Consistent Reinsurance-Investment Strategy with Delay for an Insurance under a Defaultable Market. Mathematical Analysis and Applications, 474, 1267-1288. [Google Scholar] [CrossRef] 
[14] Wang, N., Zhang, N., Jin, Z., et al. (2019) Robust Non-Zero-Sum Investment and Reinsurance Game with Default Risk. Insurance Mathematics and Economics, 84, 115-132. [Google Scholar] [CrossRef] 
[15] Grandell, J. (1991) Aspects of Risk Theory. Spring-er-Verlag, New York. [Google Scholar] [CrossRef] 
[16] Maenhout, P.J. (2004) Robust Portfolio Rules and Asset Pricing. Review of Financial Studies, 17, 951-983. [Google Scholar] [CrossRef] 

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