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Optimal proportional reinsurance to minimize the probability of drawdown under thinning-dependence structure

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  • Xia Han
  • Zhibin Liang
  • Kam Chuen Yuen

Abstract

In this paper, we consider the optimal proportional reinsurance problem in a risk model with the thinning-dependence structure, and the criterion is to minimize the probability that the value of the surplus process drops below some fixed proportion of its maximum value to date which is known as the probability of drawdown. The thinning dependence assumes that stochastic sources related to claim occurrence are classified into different groups, and that each group may cause a claim in each insurance class with a certain probability. By the technique of stochastic control theory and the corresponding Hamilton–Jacobi–Bellman equation, the optimal reinsurance strategy and the corresponding minimum probability of drawdown are derived not only for the expected value principle but also for the variance premium principle. Finally, some numerical examples are presented to show the impact of model parameters on the optimal results.

Suggested Citation

  • Xia Han & Zhibin Liang & Kam Chuen Yuen, 2018. "Optimal proportional reinsurance to minimize the probability of drawdown under thinning-dependence structure," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2018(10), pages 863-889, November.
    • Handle: RePEc:taf:sactxx:v:2018:y:2018:i:10:p:863-889
    DOI: 10.1080/03461238.2018.1469098
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    Cited by:

    1. Yuan, Yu & Han, Xia & Liang, Zhibin & Yuen, Kam Chuen, 2023. "Optimal reinsurance-investment strategy with thinning dependence and delay factors under mean-variance framework," European Journal of Operational Research, Elsevier, vol. 311(2), pages 581-595.
    2. Zhang, Caibin & Liang, Zhibin & Yuan, Yu, 2024. "Stochastic differential investment and reinsurance game between an insurer and a reinsurer under thinning dependence structure," European Journal of Operational Research, Elsevier, vol. 315(1), pages 213-227.

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