Abstract
In this paper, we investigate the extreme-value methodology, to propose an improved estimator of the conditional tail expectation (CTE) for a loss distribution with a finite mean but infinite variance.The present work introduces a new estimator of the CTE based on the bias-reduced estimators of high quantile for heavy-tailed distributions. The asymptotic normality of the proposed estimator is established and checked, in a simulation study. Moreover, we compare, in terms of bias and mean squared error, our estimator with the known old estimator.
Highlights
Introduction and MotivationRisk management is a subject of concern in finance and actuarial science
Protecting against financial and actuarial risks is essential in order to anticipate financial crises or major insurance claims
One of the best known and used risk measure is the Value-at-Risk, it is introduced in the 1990s by Morgan [27]
Summary
Risk management is a subject of concern in finance and actuarial science. Protecting against financial and actuarial risks is essential in order to anticipate financial crises or major insurance claims. We propose an improvement of the estimator established by Necir et al (2010) [28], our considerations are based on the bias-reduced estimators of high quantile for heavy-tailed distributions introduced by Li (2010) [25], we show its efficiency and its asymptotic normality theoretically, we prove the performance of our estimator by some results of simulation study. For this aim, we proceed as follow : Let X be a loss random variable with cumulative distribution function (cdf) F. The proof of the main result, which is Theorem 1 in Section 2, is postponed to Section 4
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