模糊厌恶下最小Drawdown概率的最优投资再保险策略

数学物理学报 ›› 2021, Vol. 41 ›› Issue (4): 1147-1165.

模糊厌恶下最小Drawdown概率的最优投资再保险策略

赵玉莹(),温玉珍*()

^{曲阜师范大学统计学院山东曲阜 273165}

收稿日期:2020-10-22 出版日期:2021-08-26 发布日期:2021-08-09
通讯作者: 温玉珍 E-mail:zhaoyuying95@163.com;wenyzhen@163.com
作者简介:赵玉莹, E-mail: zhaoyuying95@163.com
基金资助:
国家自然科学基金(11501319);中国博士后科学基金(2015M582064);山东省自然科学基金(ZR-2020MA035);山东省自然科学基金(ZR2015AL013)

Optimal Investment and Proportional Reinsurance Strategies to Minimize the Probability of Drawdown Under Ambiguity Aversion

Yuying Zhao(),Yuzhen Wen*()

^{School of Statistics, Qufu Normal University, Shandong Qufu 273165}

Received:2020-10-22 Online:2021-08-26 Published:2021-08-09
Contact: Yuzhen Wen E-mail:zhaoyuying95@163.com;wenyzhen@163.com
Supported by:
the NSFC(11501319);the China Postdoctoral Science Foundation(2015M582064);the NSF of Shandong Province(ZR-2020MA035);the NSF of Shandong Province(ZR2015AL013)

摘要/Abstract

摘要：

该文考虑了模糊厌恶下保险公司的最优投资和再保险问题，得到了保险市场和金融市场均存在模糊厌恶时，保险公司盈余的最小drawdown概率及其最优鲁棒投资和再保险策略的解析解.通过数值分析得出一些重要参数对值函数的影响.

关键词: 模糊厌恶, drawdown概率, 最优鲁棒投资再保险策略, 扭曲漂移

Abstract:

In this paper, we consider the optimal investment and reinsurance control problem for insurers with ambiguity, and we obtain the minimum drawdown probability, optimal robust investment-reinsurance strategies and the associated drift distortion. Moreover, some numerical examples are presented to show the impact of model parameters on the optimal results.

Key words: Ambiguity aversion, Probability of drawdown, Optimal robust investment and reinsurance strategies, Drift distortion

中图分类号:

O224

赵玉莹,温玉珍. 模糊厌恶下最小Drawdown概率的最优投资再保险策略[J]. 数学物理学报, 2021, 41(4): 1147-1165.

Yuying Zhao,Yuzhen Wen. Optimal Investment and Proportional Reinsurance Strategies to Minimize the Probability of Drawdown Under Ambiguity Aversion[J]. Acta mathematica scientia,Series A, 2021, 41(4): 1147-1165.

图/表 3

参考文献 16

1	Browne S . Optimal investment policies for a firm with a random risk process: exponential utility and minimizing the probability of ruin. Math Oper Res, 1995, 20, 937- 958 doi: 10.1287/moor.20.4.937
2	Bai L , Guo J . Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint. Insur Math Econ, 2008, 42 (3): 968- 975 doi: 10.1016/j.insmatheco.2007.11.002
3	Liang Z , Bai L , Guo J . Optimal investment and proportional reinsurance with constrained control variables. Optim Contr Appl Met, 2011, 32 (5): 587- 608 doi: 10.1002/oca.965
4	陈密, 郭军义. 指数保费准则下的最优投资和比例再保险. 数学物理学报, 2014, 34A (5): 1161- 1172
	Chen M , Guo J . Optiaml investment and proportional reinsurance under exponential premium calculation. Acta Math Sci, 2014, 34A (5): 1161- 1172
5	Maenhout P J . Robust portfolio rules and asset pricing. Rev Financ Stud, 2004, 17 (4): 951- 983 doi: 10.1093/rfs/hhh003
6	Bordigoni G, Matoussi A, Schweizer M. A Stochastic Control Approach to a Robust Utility Maximization Problem//Benth F E, Di Nunno G, Lindstrom T, et al. Stoch Anal Appl. Berlin: Springer, 2007: 125-151
7	李冰, 耿彩霞. CEV模型下鲁棒最优投资和超额损失再保险问题研究. 统计学与应用, 2018, 7 (5): 495- 504
	Li B , Geng C . Research on robust optimal investment and excess-of-loss reinsurance under CEV model. Statistics and Applications, 2018, 7 (5): 495- 504
8	Liu B , Zhou M , Li P . Optimal investment and premium control for insurers with ambiguity. Commun Stat Theor M, 2020, 49 (9): 2110- 2130 doi: 10.1080/03610926.2019.1568487
9	Bayraktar E , Zhang Y . Minimizing the probability of lifetime ruin under ambiguity aversion. SIAM J. Control Optim, 2015, 53 (1): 58- 90 doi: 10.1137/140955999
10	Schmidli H . Optimal proportional reinsurance policies in a dynamic setting. Scand Actuar J, 2001, 2001 (1): 55- 68 doi: 10.1080/034612301750077338
11	Young V . Optimal investmet strategy to minimize the probability of lifetime ruin. North Amer Actuar J, 2004, 8 (4): 105- 126
12	David P S , Young V R . Minimizing the probability of ruin when claims follow Brownian motion with drift. North Amer Actuar J, 2005, 9 (3): 110- 128 doi: 10.1080/10920277.2005.10596214
13	Angoshtari B , Bayraktar E , Young V . Optimal investment to minimize the probability of drawdown. Stochastics, 2016, 88 (6): 946- 958 doi: 10.1080/17442508.2016.1155590
14	Han X , Liang Z , Yuen K C . Optimal proportional reinsurance to minimize the probability of drawdown under thinning-dependence structure. Scand Actuar J, 2018, 10, 863- 889
15	Angoshtari B , Bayraktar E , Young V . Minimizing the probability of lifetime drawdown under constant consumption. Insur Math Econ, 2016, 69, 210- 223 doi: 10.1016/j.insmatheco.2016.05.007
16	Han X , Liang Z . Optimal reinsurance and investment in danger-region and safe-region. Optim Contr Appl Met, 2020, 41, 765- 792 doi: 10.1002/oca.2568

[1]	谢亚君. 一类基于Halley-Newton型的有效修正算法[J]. 数学物理学报, 2021, 41(4): 1066-1078.
[2]	冯欣怡,孙祥凯. 一类带DC函数的分式优化的Farkas引理刻画[J]. 数学物理学报, 2021, 41(3): 827-836.
[3]	张晶,余旌胡. 线性回归模型参数估计方法的分辨率[J]. 数学物理学报, 2020, 40(5): 1381-1392.
[4]	叶冬平,方东辉. 鲁棒复合优化问题的Lagrange对偶[J]. 数学物理学报, 2020, 40(4): 1095-1107.
[5]	李萌,余国林. 不确定凸优化问题鲁棒近似解的最优性[J]. 数学物理学报, 2020, 40(4): 1007-1017.
[6]	方东辉,田利萍,王仙云. 复合凸优化问题的Fenchel-Lagrange强对偶之研究[J]. 数学物理学报, 2020, 40(1): 20-30.
[7]	孙祥凯. 不确定信息下凸优化问题的鲁棒解刻划[J]. 数学物理学报, 2017, 37(2): 257-264.
[8]	李英毅, 张海斌, 高欢. 一类修正邻近梯度法及其收敛性[J]. 数学物理学报, 2015, 35(6): 1136-1145.
[9]	黄正刚. 一种新的广义次梯度及其性质[J]. 数学物理学报, 2015, 35(5): 927-935.
[10]	张运胜, 高雷阜. 对称锥互补问题的一种非精确光滑牛顿算法[J]. 数学物理学报, 2015, 35(4): 824-832.