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 \(F_X(x)=P(X\le x)\) 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.
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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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Du, J., Li, Z. & Wu, L. Optimal Stop-Loss Reinsurance Under the VaR and CTE Risk Measures: Variable Transformation Method. Comput Econ 53, 1133–1151 (2019). https://doi.org/10.1007/s10614-017-9778-1
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DOI: https://doi.org/10.1007/s10614-017-9778-1