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Stochastic differential investment-reinsurance games with capital injection-barrier dividend(PDF)


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Stochastic differential investment-reinsurance games with capital injection-barrier dividend
Sun Zongqi1 Liu Xuanhui2 Chen Siyuan1 Ji Yongqiang1 and Lou Jianjun1
1) Department of Mathematics, Xi’an Siyuan University, Xi’an 710038, Shaanxi Province, P.R.China
2) College of Science, Xi’ an Polytechnic University, Xi’an 710048, Shaanxi Province, P.R.China
operations research game theory stochastic differential game Hamilton-Jacobi-Bellman-Isaacs equation investment strategies proportional reinsurance capital injection-barrier dividend model risk
O 211.63
To better reflect the insurance practice and help insurance company make more robust strategy, we investigate the optimal investment-reinsurance-capital injection-barrier dividend problem when model risk exists. Based on the criterion of maximizing the expected total present value of the difference between barrier dividend and capital injection, the stochastic differential game model is utilized based on stochastic differential game principle, and the optimal policy is obtained by solving the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation. The closed-form optimal investment-reinsurance-capital injection-barrier dividend strategies are derived. The economic analyses illustrate the reasonableness of the obtained theoretical results.


[1] Asmussen S, Tacksar M. Controlled diffusion models for optimal dividend pay-out[J]. Insurance: Mathematics and Economics, 1997, 20(1): 1-15.
[2] Hojgaard B. Optimal dividend pay-out with the option of proportional reinsurance in the diffusion model[J]. Insuranse: Mathematics and Economics, 1997, 20(2): 151.
[3] Schmidli H. Optimal proportional reinsurance policies in a dynamic setting[J]. Scandinavian Actuarial Journal, 2001, 2001(1): 55-68.
[4] Isaacs R. Differential games[M]. New York: Wiley, 1965.
[5] Elliote R. The existence of value in stochastic differential games[J]. SIAM Journal on Control and Optimization, 1976, 14(1): 85-94.
[6] Taksar M,Zeng Xudong. Optimal nonproportional reinsurance control and stochastic differential games[J].Insurance:Mathematics and Economics, 2011, 48(1):64-71.
[7] Bensoussan A, Siu C C, Yam S C P, et al. A class of non-zero-sum stochastic differential investment and reinsurance games[J]. Automatica, 2014, 50(8): 2025-2037.
[8] Zeng Xudong. Optimal reinsurance with a rescuing procedure[J]. Insurance: Mathematics and Economics, 2010, 46(2): 397-405.
[9] Zeng Xudong.A stochastic differential reinsurance games[J]. Journal of Applied Probability, 2010, 47(2): 335-349.
[10] Lin Xiang, Zhang Chunhong, Siu T K. Stochastic differential portfolios games for an insurer in a jump-diffusion risk process[J]. Mathematics Method of Operations Research, 2012, 75(1): 83-100.
[11] 罗琰,杨招军.基于随机微分博弈的保险公司最优决策模型[J].保险研究,2011,8(20):48-52.
 Luo Yan, Yang Zhaojun. Optimal strategy of insurer based on stochastic differential[J]. Insurance Studies, 2010, 8(20):48-52.(in Chinese)
[12] 杨鹏,林祥.随机微分博弈下的资产负债管理[J].中山大学学报自然科学版,2013,52(6):30-34.
Yang Peng, Lin Xiang. Asset and liability management under stochastic differential games[J]. Acta Scientiarum Naturalium Universitaties Sunyetseni, 2013, 52(6): 30-33.(in Chinese)
[13] 杨鹏.基于再保险和投资的随机微分博弈[J].数学杂志,2014,34(4):779-786.
Yang Peng. Stochastic differential games with reinsurance and investment[J]. Journal of Mathematics, 2014, 34(2): 779-786.(in Chinese)
[14] Sethis S P, Taksar M I.Optimal financing of a corporation subject to random returns[J]. Mathematical Finance, 2002,1(12): 155-172.
[15] Dickson D C M, Waters H R. Some optimal dividend problems[J]. ASTIN Bulletin: the Journal of the International Actuarial Association, 2004, 34(1): 49-74.
[16] Gerber H U, Shiu E S W. On optimal dividend strategies in the compound Poisson model[J]. North American Actuarial Journal, 2006, 10(2): 76-93.
[17] 张帅琪,刘国欣.带注资的二维复合泊松模型的最优分红[J].运筹学学报,2012,16(3):119-131.
Zhang Shuaiqi, Liu Guoxin. Optimal dividend payments of the two-dimensional compound Poisson risk model with capital injection[J]. Operations Research Transactions, 2012, 16(3): 119-131.(in Chinese)
[18] 王永茂,祁晓玉,贠小青.基于经典风险模型的最优分红和最优注资策略研究[J].郑州大学学报理学版,2015,47(2):37-40.
Wang Yongmao, Qi Xiaoyu, Yun Xiaoqing. Optimal dividend capital injection strategy in classical risk model[J]. Journal of Zhengzhou University Natural Science Edition, 2015, 47(2): 37-40.(in Chinese)
[19] Taksar M I, Markussen C. Optimal dynamic reinsurance policies for large insurance portfolios[J]. Finance and Stochastics, 2003, 7(1): 97-121.
[20] Mataramvura S, ksendal B. Risk minimizing portfolios and HJBI equations for stochastic differential games[J]. Stochastics: an International Journal of Probability and Stochastic Processes, 2008, 80(4): 317-337.
[21] 孙宗岐,刘宣会,陈思源,等.动态VaR约束下带有界分红的最优再保策略[J].云南民族大学学报自然科学版,2016,25(5):463-468.
Sun Zongqi, Liu Xuanhui, Chen Siyuan, Ji Yongqiang. Optimal reinsurance approach with barrier dividend under dynamic VaR constraint[J]. Journal of Yunnan University of Nationalities Natural Sciences Edition, 2016, 25(5): 463-468.(in Chinese)


Last Update: 2017-06-26