Asymptotic theory for the empirical Haezendonck–Goovaerts risk measure |
| |
Institution: | 1. Department of Statistics, Ewha Womans University, 11-1 Daehyun-Dong, Seodaemun-Gu, Seoul 120-750, Republic of Korea;2. Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, United States;1. University of Southern California, United States;2. Singapore Management University, Singapore;1. Cass Business School, City, University of London, United Kingdom;2. DEAMS, University of Trieste, Italy;1. Norwegian University of Science and Technology (NTNU), Norway;2. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, United States |
| |
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. |
| |
Keywords: | Orlicz premium Tail value-at-Risk (T-VaR) Conditional tail expectation (CTE) Empirical CTE |
本文献已被 ScienceDirect 等数据库收录! |
|