Journal of Probability and Statistics
Volume 2010 (2010), Article ID 596839, 17 pages
doi:10.1155/2010/596839
Research Article

Estimating the Conditional Tail Expectation in the Case of Heavy-Tailed Losses

Abdelhakim Necir,1 Abdelaziz Rassoul,2 and Ričardas Zitikis3

1Laboratory of Applied Mathematics, Mohamed Khider University of Biskra, 07000, Algeria
2Ecole Nationale Superieure d'Hydraulique, Guerouaou, BP 31, Blida, 09000, Algeria
3Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON, N6A5B7, Canada

Received 21 October 2009; Accepted 20 January 2010

Academic Editor: Edward Furman

Copyright © 2010 Abdelhakim Necir et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The conditional tail expectation (CTE) is an important actuarial risk measure and a useful tool in financial risk assessment. Under the classical assumption that the second moment of the loss variable is finite, the asymptotic normality of the nonparametric CTE estimator has already been established in the literature. The noted result, however, is not applicable when the loss variable follows any distribution with infinite second moment, which is a frequent situation in practice. With a help of extreme-value methodology, in this paper, we offer a solution to the problem by suggesting a new CTE estimator, which is applicable when losses have finite means but infinite variances.