Journal article
Asymptotic theory for the empirical Haezendonck–Goovaerts risk measure
Insurance, mathematics & economics, Vol.55(1), pp.78-90
03/2014
DOI: 10.1016/j.insmatheco.2013.12.003
Abstract
Haezendonck–Goovaerts risk measures is a recently introduced class of risk measures which includes, as its minimal member, the Tail Value-at-Risk (T-VaR)—T-VaR arguably the most popular risk measure in global insurance regulation. In applications often one has to estimate the risk measure given a random sample from an unknown distribution. The distribution could either be truly unknown or could be the distribution of a complex function of economic and idiosyncratic variables with the complexity of the function rendering indeterminable its distribution. Hence statistical procedures for the estimation of Haezendonck–Goovaerts risk measures are a key requirement for their use in practice. A natural estimator of the Haezendonck–Goovaerts risk measure is the Haezendonck–Goovaerts risk measure of the empirical distribution, but its statistical properties have not yet been explored in detail. The main goal of this article is to both establish the strong consistency of this estimator and to derive weak convergence limits for this estimator. We also conduct a simulation study to lend insight into the sample sizes required for these asymptotic limits to take hold. •We study the non-parametric estimation of the Haezendonck Risk Measure via the empirical Haezendonck risk measure.•We provide a strong consistency result for the empirical Haezendonck risk measure.•We also provide a weak convergence result for the empirical Haezendonck risk measure.
Details
- Title: Subtitle
- Asymptotic theory for the empirical Haezendonck–Goovaerts risk measure
- Creators
- Jae Youn Ahn - Department of Statistics, Ewha Womans University, 11-1 Daehyun-Dong, Seodaemun-Gu, Seoul 120-750, Republic of KoreaNariankadu D Shyamalkumar - Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, United States
- Resource Type
- Journal article
- Publication Details
- Insurance, mathematics & economics, Vol.55(1), pp.78-90
- Publisher
- Elsevier B.V
- DOI
- 10.1016/j.insmatheco.2013.12.003
- ISSN
- 0167-6687
- eISSN
- 1873-5959
- Language
- English
- Date published
- 03/2014
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9983985987202771
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