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Optimal Stop-Loss Reinsurance Under the VaR and CTE Risk Measures: Variable Transformation Method

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  • Junhong Du

    (Xinjiang University)

  • Zhiming Li

    (Xinjiang University)

  • Lijun Wu

    (Xinjiang University)

Abstract

In this paper, we propose a variable transformation way and obtain the optimal stop-loss reinsurance under value at risk (VaR) and conditional tail expectation (CTE) criteria, respectively. Let X be the initial loss of an insurer with cumulative distribution function $$F_X(x)=P(X\le x)$$FX(x)=P(X≤x) and survival function $$S_X(x)=1-F_X(x)$$SX(x)=1-FX(x). Denote a transformation variable $$Y=-\,\ln (S_X(X))$$Y=-ln(SX(X)). Firstly, we analyze properties of the variables X and Y. Then, under VaR- and CTE-optimization criteria, we provide the necessary and sufficient conditions for the optimal retention existence of Y, respectively. Further, the optimal retention of X is obtained. Some examples are given to illustrate these results.

Suggested Citation

  • Junhong Du & Zhiming Li & Lijun Wu, 2019. "Optimal Stop-Loss Reinsurance Under the VaR and CTE Risk Measures: Variable Transformation Method," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1133-1151, March.
    • Handle: RePEc:kap:compec:v:53:y:2019:i:3:d:10.1007_s10614-017-9778-1
    DOI: 10.1007/s10614-017-9778-1
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    References listed on IDEAS

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    2. Khreshna Syuhada & Arief Hakim & Suci Sari, 2021. "The Combined Stop-Loss and Quota-Share Reinsurance: Conditional Tail Expectation-Based Optimization from the Joint Perspective of Insurer and Reinsurer," Risks, MDPI, vol. 9(7), pages 1-21, July.

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