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Optimal Dividend-Penalty Strategies for Insurance Risk Models with Surplus-Dependent Premiums

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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.

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Authors and Affiliations

  1. School of Economics and Management, Hebei University of Technology, Tianjin, 300401, China

    Jingwei Li  (李静伟)

  2. Department of Applied Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Guoxin Liu  (刘国欣)

  3. School of Science, Hebei University of Technology, Tianjin, 300401, China

    Jinyan Zhao  (赵锦艳)

Authors
  1. Jingwei Li  (李静伟)
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  2. Guoxin Liu  (刘国欣)
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  3. Jinyan Zhao  (赵锦艳)
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Corresponding author

Correspondence to Jinyan Zhao  (赵锦艳).

Additional information

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).

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Li, J., Liu, G. & Zhao, J. Optimal Dividend-Penalty Strategies for Insurance Risk Models with Surplus-Dependent Premiums. Acta Math Sci 40, 170–198 (2020). https://doi.org/10.1007/s10473-020-0112-1

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  • DOI: https://doi.org/10.1007/s10473-020-0112-1

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