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

doi:10.1007/s10473-020-0112-1

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (1): 170-198.doi: 10.1007/s10473-020-0112-1

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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).

Abstract

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

CLC Number:

91B30

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

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