OPTIMAL DIVIDEND-PENALTY STRATEGIES FOR INSURANCE RISK MODELS WITH SURPLUS-DEPENDENT PREMIUMS

doi:10.1007/s10473-020-0112-1

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (1): 170-198.doi: 10.1007/s10473-020-0112-1

OPTIMAL DIVIDEND-PENALTY STRATEGIES FOR INSURANCE RISK MODELS WITH SURPLUS-DEPENDENT PREMIUMS

李静伟¹, 刘国欣², 赵锦艳³

1. School of Economics and Management, Hebei University of Technology, Tianjin 300401, China;
2. Department of Applied Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
3. School of Science, Hebei University of Technology, Tianjin 300401, China

收稿日期:2018-10-25 修回日期:2019-02-23 出版日期:2020-02-25 发布日期:2020-04-14
通讯作者: Jinyan ZHAO E-mail:zhaojinyan@hebut.edu.cn
基金资助:
This work was supported by National Natural Science Foundation of China (11471218), Hebei Higher School Science and Technology Research Projects (ZD20131017), Joint Doctoral Training Foundation of HEBUT (2018GN0001).

OPTIMAL DIVIDEND-PENALTY STRATEGIES FOR INSURANCE RISK MODELS WITH SURPLUS-DEPENDENT PREMIUMS

Jingwei LI¹, Guoxin LIU², Jinyan ZHAO³

1. School of Economics and Management, Hebei University of Technology, Tianjin 300401, China;
2. Department of Applied Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
3. School of Science, Hebei University of Technology, Tianjin 300401, China

Received:2018-10-25 Revised:2019-02-23 Online:2020-02-25 Published:2020-04-14
Contact: Jinyan ZHAO E-mail:zhaojinyan@hebut.edu.cn
Supported by:
This work was supported by National Natural Science Foundation of China (11471218), Hebei Higher School Science and Technology Research Projects (ZD20131017), Joint Doctoral Training Foundation of HEBUT (2018GN0001).

摘要/Abstract

摘要： This paper concerns an optimal dividend-penalty problem for the risk models with surplus-dependent premiums. The objective is to maximize the difference of the expected cumulative discounted dividend payments received until the moment of ruin and a discounted penalty payment taken at the moment of ruin. Since the value function may be not smooth enough to be the classical solution of the HJB equation, the viscosity solution is involved. The optimal value function can be characterized as the smallest viscosity supersolution of the HJB equation and the optimal dividend-penalty strategy has a band structure. Finally, some numerical examples with gamma distribution for the claims are analyzed.

关键词: band strategy, risk models with surplus-dependent premiums, HJB equation, viscosity solution, Gerber-shiu function

Abstract: This paper concerns an optimal dividend-penalty problem for the risk models with surplus-dependent premiums. The objective is to maximize the difference of the expected cumulative discounted dividend payments received until the moment of ruin and a discounted penalty payment taken at the moment of ruin. Since the value function may be not smooth enough to be the classical solution of the HJB equation, the viscosity solution is involved. The optimal value function can be characterized as the smallest viscosity supersolution of the HJB equation and the optimal dividend-penalty strategy has a band structure. Finally, some numerical examples with gamma distribution for the claims are analyzed.

Key words: band strategy, risk models with surplus-dependent premiums, HJB equation, viscosity solution, Gerber-shiu function

中图分类号:

91B30

李静伟, 刘国欣, 赵锦艳. OPTIMAL DIVIDEND-PENALTY STRATEGIES FOR INSURANCE RISK MODELS WITH SURPLUS-DEPENDENT PREMIUMS[J]. 数学物理学报(英文版), 2020, 40(1): 170-198.

Jingwei LI, Guoxin LIU, Jinyan ZHAO. OPTIMAL DIVIDEND-PENALTY STRATEGIES FOR INSURANCE RISK MODELS WITH SURPLUS-DEPENDENT PREMIUMS[J]. Acta mathematica scientia,Series B, 2020, 40(1): 170-198.

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OPTIMAL DIVIDEND-PENALTY STRATEGIES FOR INSURANCE RISK MODELS WITH SURPLUS-DEPENDENT PREMIUMS

OPTIMAL DIVIDEND-PENALTY STRATEGIES FOR INSURANCE RISK MODELS WITH SURPLUS-DEPENDENT PREMIUMS

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