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Optimal proportional reinsurance with common shock dependence to minimise the probability of drawdown

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  • Han, Xia
  • Liang, Zhibin
  • Zhang, Caibin

Abstract

In this paper, we study the optimal proportional reinsurance problem in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component, and the criterion is to minimise the probability of drawdown, namely, the probability that the value of the surplus process reaches some fixed proportion of its maximum value to date. By the method of maximising the ratio of drift of a diffusion divided to its volatility squared, and the technique of stochastic control theory and the corresponding Hamilton–Jacobi–Bellman equation, we investigate the optimisation problem in two different cases. Furthermore, we constrain the reinsurance proportion in the interval [0,1] for each case, and derive the explicit expressions of the optimal proportional reinsurance strategy and the minimum probability of drawdown. Finally, some numerical examples are presented to show the impact of model parameters on the optimal results.

Suggested Citation

  • Han, Xia & Liang, Zhibin & Zhang, Caibin, 2019. "Optimal proportional reinsurance with common shock dependence to minimise the probability of drawdown," Annals of Actuarial Science, Cambridge University Press, vol. 13(2), pages 268-294, September.
    • Handle: RePEc:cup:anacsi:v:13:y:2019:i:02:p:268-294_00
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    Citations

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    Cited by:

    1. Leonie Violetta Brinker, 2021. "Minimal Expected Time in Drawdown through Investment for an Insurance Diffusion Model," Risks, MDPI, vol. 9(1), pages 1-18, January.
    2. 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.
    3. Yu Yuan & Zhibin Liang & Xia Han, 2022. "Minimizing the penalized probability of drawdown for a general insurance company under ambiguity aversion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(2), pages 259-290, October.
    4. Liang, Xiaoqing & Liang, Zhibin & Young, Virginia R., 2020. "Optimal reinsurance under the mean–variance premium principle to minimize the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 128-146.
    5. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2021. "Optimal Reinsurance and Investment under Common Shock Dependence Between Financial and Actuarial Markets," Papers 2105.07524, arXiv.org.

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