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Optimal per-loss reinsurance and investment to minimize the probability of drawdown

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  • Xia Han
  • Zhibin Liang

Abstract

In this paper, we study an optimal reinsurance-investment 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. We assume that the insurer can purchase per-loss reinsurance for each line of business and invest its surplus in a financial market consisting of a risk-free asset and a risky asset. Under the criterion of minimizing the probability of drawdown, the closed-form expressions of the optimal reinsurance-investment strategy and the corresponding value function are obtained. We show that the optimal reinsurance strategy is in the form of pure excess-of-loss reinsurance strategy under the expected value principle, and under the variance premium principle, the optimal reinsurance strategy is in the form of pure quota-share reinsurance. Furthermore, we extend our model to the case where the insurance company involves $n$ $(n\geq3)$ dependent classes of insurance business and the optimal results are derived explicitly as well.

Suggested Citation

  • Xia Han & Zhibin Liang, 2020. "Optimal per-loss reinsurance and investment to minimize the probability of drawdown," Papers 2010.12158, arXiv.org.
  • Handle: RePEc:arx:papers:2010.12158
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    Cited by:

    1. Ling Wang & Mei Choi Chiu & Hoi Ying Wong, 2021. "Time-consistent mean-variance reinsurance-investment problem with long-range dependent mortality rate," Papers 2112.06602, arXiv.org.
    2. Li, Danping & Young, Virginia R., 2021. "Bowley solution of a mean–variance game in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 35-43.

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