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Ruin Minimization for Insurers with Borrowing Constraints

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  • Shangzhen Luo

Abstract

We consider an optimal dynamic control problem for an insurance company with opportunities of proportional reinsurance and investment. The company can purchase proportional reinsurance to reduce its risk level and invest its surplus in a financial market that has a Black-Scholes risky asset and a risk-free asset. When investing in the risk-free asset, three practical borrowing constraints are studied individually: (B1) the borrowing rate is higher than lending (saving) rate, (B2) the dollar amount borrowed is no more than K > 0, and (B3) the proportion of the borrowed amount to the surplus level is no more than k > 0. Under each of the constraints, the objective is to minimize the probability of ruin. Classical stochastic control theory is applied to solve the problem. Specifically, the minimal ruin probability functions are obtained in closed form by solving Hamilton-Jacobi-Bellman (HJB) equations, and their associated optimal reinsurance-investment policies are found by verification techniques.

Suggested Citation

  • Shangzhen Luo, 2008. "Ruin Minimization for Insurers with Borrowing Constraints," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(2), pages 143-174.
    • Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:143-174
    DOI: 10.1080/10920277.2008.10597508
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    Cited by:

    1. Hiroaki Hata & Shuenn-Jyi Sheu & Li-Hsien Sun, 2019. "Expected exponential utility maximization of insurers with a general diffusion factor model : The complete market case," Papers 1903.08957, arXiv.org.
    2. Azcue, Pablo & Muler, Nora, 2009. "Optimal investment strategy to minimize the ruin probability of an insurance company under borrowing constraints," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 26-34, February.
    3. Tatiana Belkina & Christian Hipp & Shangzhen Luo & Michael Taksar, 2011. "Optimal Constrained Investment in the Cramer-Lundberg model," Papers 1112.4007, arXiv.org.
    4. Yakun Liu & Jingchao Li & Jieming Zhou & Yingchun Deng, 2024. "Optimal Investment and Reinsurance to Maximize the Probability of Drawup Before Drawdown," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-34, September.
    5. Hiroaki Hata & Kazuhiro Yasuda, 2024. "Expected Power Utility Maximization of Insurers," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 31(3), pages 543-577, September.

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