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

Junhong Du (), Zhiming Li () and Lijun Wu ()
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Junhong Du: Xinjiang University
Zhiming Li: Xinjiang University
Lijun Wu: Xinjiang University

Computational Economics, 2019, vol. 53, issue 3, No 11, 1133-1151

Abstract: 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.

Keywords: Stop-loss reinsurance; Expected value principle; Value at risk (VaR); Conditional tail expectation (CTE); Variable transformation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10614-017-9778-1

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