Computational Economics

, Volume 53, Issue 3, pp 1133–1151 | Cite as

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

  • Junhong Du
  • Zhiming Li
  • Lijun WuEmail author


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 \(F_X(x)=P(X\le x)\) and survival function \(S_X(x)=1-F_X(x)\). Denote a transformation variable \(Y=-\,\ln (S_X(X))\). 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.


Stop-loss reinsurance Expected value principle Value at risk (VaR) Conditional tail expectation (CTE) Variable transformation 



This work is supported by the Natural Science Foundation of Xinjiang (Grant No. 2016D01C043) and the Natural Science Foundation of China (Grant Nos. 11361058, 11661076).


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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.College of Mathematics and System ScienceXinjiang UniversityUrumqiPeople’s Republic of China

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