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Optimal dynamic reinsurance with dependent risks: variance premium principle

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  • Zhibin Liang
  • Kam Chuen Yuen

Abstract

In this paper, we consider the optimal proportional reinsurance strategy in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. Under the criterion of maximizing the expected exponential utility with the variance premium principle, we adopt a nonstandard approach to examining the existence and uniqueness of the optimal reinsurance strategy. Using the technique of stochastic control theory, closed-form expressions for the optimal strategy and the value function are derived for the compound Poisson risk model as well as for the Brownian motion risk model. From the numerical examples, we see that the optimal results for the compound Poisson risk model are very different from those for the diffusion model. The former depends not only on the safety loading, time, and the interest rate, but also on the claim size distributions and the claim number processes, while the latter depends only on the safety loading, time, and the interest rate.

Suggested Citation

  • Zhibin Liang & Kam Chuen Yuen, 2016. "Optimal dynamic reinsurance with dependent risks: variance premium principle," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(1), pages 18-36, January.
    • Handle: RePEc:taf:sactxx:v:2016:y:2016:i:1:p:18-36
    DOI: 10.1080/03461238.2014.892899
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    Cited by:

    1. Zhang, Yawen & Zhang, Caibin, 2024. "Stackelberg differential reinsurance and investment game for a dependent risk model with Ornstein–Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 214(C).
    2. Zongxia Liang & Yi Xia & Bin Zou, 2024. "A Two-layer Stochastic Game Approach to Reinsurance Contracting and Competition," Papers 2405.06235, arXiv.org, revised Sep 2024.
    3. Yan Zhang & Peibiao Zhao & Rufei Ma, 2022. "Robust Optimal Excess-of-Loss Reinsurance and Investment Problem with more General Dependent Claim Risks and Defaultable Risk," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2743-2777, December.

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