损失规避行为下的一般保险公司最优投资再保险问题
Optimal Investment and Reinsurance Problem for a General Insurance Company under Behavior of Loss Aversion
摘要: 本文研究的是基于损失规避的一般保险公司(包括保险公司和再保险公司)的最优投资再保险问题。管理者管理风险通过购买比例再保险和投资金融市场。假设索赔过程服从一个带漂移项的布朗运动，保费率采用期望值原则。保险公司和再保险公司在金融市场中都被允许投资无风险资产和风险资产。风险资产的价格过程服从跳扩散过程。目标是最大化保险公司和再保险公司的共同利益，即最大化财富过程权重和的S-型期望效应。应用鞅方法，我们推导出最优财富过程权重和及相应的最优策略。最后，我们通过数值例子说明模型的参数对最优策略的影响。
Abstract: In the paper, we study the optimal investment reinsurance problem for general insurance companies (insurance company and reinsurance company) based on behavior of loss aversion. Managers manage risk by purchasing proportional reinsurance and investing in financial markets. Assume that the claim process is described by a Brownian motion with drift. The premium rate is calculated through the expectation principle. Both insurance company and reinsurance company are allowed to invest in risk-free assets and risky assets. The price process of risk assets is subject to a jump-diffusion process. Our goal is to maximize the common interests of insurance company and reinsurance company, i.e. Maximizing the weight sum of the wealth process. Using the martingale method, we derive the closed expression of the optimal wealth process weight and its corresponding optimal investment reinsurance strategies. Finally, numerical examples are provided to show the impact of model parameters on the optimal strategies.
文章引用：耿彩霞, 李冰. 损失规避行为下的一般保险公司最优投资再保险问题[J]. 统计学与应用, 2020, 9(2): 149-162. https://doi.org/10.12677/SA.2020.92017

参考文献

[1] Zhang, Q. and Chen, P. (2019) Robust Optimal Proportional Reinsurance and Investment Strategy for an Insurer with Defaultable Risks and Jumps. Journal of Computational and Applied Mathematics, 356, 46-66. [Google Scholar] [CrossRef] 
[2] Yang, H.L. and Zhang, L.H. (2005) Optimal Investment for Insurer with Jump-Diffusion Risk Process. Insurance Mathematics and Economics, 37, 615-634. [Google Scholar] [CrossRef] 
[3] Browne, S. (1995) Optimal Investment Policies for a Firm with Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin. Mathematics of Operations Research, 20, 937-958. [Google Scholar] [CrossRef] 
[4] Bai, L.H. and Guo, J.Y. (2008) Optimal Proportional Reinsurance and Investment with Multiple Risky Assets and No-Shorting Constraint. Insurance Mathematics and Economics, 42, 968-975. [Google Scholar] [CrossRef] 
[5] Zhang, X., Meng, H. and Zenf, Y. (2016) Optimal Investment and Reinsurance Strategies for Insurers with Generalized Mean-Variance Premium Principle and No-Short Selling. Insurance Mathematics and Economics, 67, 125-132. [Google Scholar] [CrossRef] 
[6] Shen, Y. and Zeng, Y. (2015) Optimal Invest-ment-Reinsurance Strategy for Mean-Variance Insurers with Square-Root Factor Process. Insurance Mathematics and Economics, 62, 118-137. [Google Scholar] [CrossRef] 
[7] Wu, H.L. and Zeng, Y. (2015) Equilibrium Investment Strategy for Deined-Contribution Pension Schemes with Generalized Mean-Variance Criterion and Mortality Risk. Insurance Mathematics and Economics, 64, 396-408. [Google Scholar] [CrossRef] 
[8] Zhang, C.B. and Liang, Z.B. (2016) Portfolio Optimization for Jump-Diffusion Risky Assets with Common Shock Dependence and State Dependent Risk Aversion. Optimal Control Applications and Methods, 38, 229-246. [Google Scholar] [CrossRef] 
[9] Tversky, A. and Kahnean, D. (1992) Advances in Prospect Theory: Cumulative Representation of Uncertainty. Journal of Risk and Uncertainty, 5, 297-323. [Google Scholar] [CrossRef] 
[10] Berkelaar, A.B., Kouwenberg, R. and Post, T. (2004) Optimal Portfolio Choice under Loss Aversion. Review of Economics and Statistics, 86, 973-987. [Google Scholar] [CrossRef] 
[11] Dong, Y.H. and Zheng, H. (2019) Optimal Investment of DC Pension Plan under Short-Selling Constraints and Portfolio Insurance. Insurance Mathematics and Economics, 85, 47-59. [Google Scholar] [CrossRef] 
[12] 郭文旌. 基于损失规避行为的最优保险投资与再保险策略选择[J]. 系统科学与数学, 2018, 38(9): 1005-1017.
[13] Oksendal, B. and Sulem, A. (2005) Applied Stochastic Control of Jump Diffusions. Springer, Berlin.
[14] Guo, W.J. (2014) Optimal Portfolio Choice for an Insurer with Loss Aversion. Insurance Mathematics and Economics, 58, 217-222. [Google Scholar] [CrossRef] 

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