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Optimal Insurance to Minimize the Probability of Ruin: Inverse Survival Function Formulation

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  • Bahman Angoshtari
  • Virginia R. Young

Abstract

We find the optimal indemnity to minimize the probability of ruin when premium is calculated according to the distortion premium principle with a proportional risk load, and admissible indemnities are such that both the indemnity and retention are non-decreasing functions of the underlying loss. We reformulate the problem with the inverse survival function as the control variable and show that deductible insurance with maximum limit is optimal. Our main contribution is in solving this problem via the inverse survival function.

Suggested Citation

  • Bahman Angoshtari & Virginia R. Young, 2020. "Optimal Insurance to Minimize the Probability of Ruin: Inverse Survival Function Formulation," Papers 2012.03798, arXiv.org.
    • Handle: RePEc:arx:papers:2012.03798
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    References listed on IDEAS

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    1. Cai, Jun & Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2008. "Optimal reinsurance under VaR and CTE risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 185-196, August.
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    6. Zhuang, Sheng Chao & Weng, Chengguo & Tan, Ken Seng & Assa, Hirbod, 2016. "Marginal Indemnification Function formulation for optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 65-76.
    7. Chi, Yichun & Tan, Ken Seng, 2011. "Optimal Reinsurance under VaR and CVaR Risk Measures: a Simplified Approach," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 487-509, November.
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