Title
How to estimate the value at risk under incomplete information How to estimate the value at risk under incomplete information
Author
Faculty/Department
Faculty of Applied Economics
Publication type
article
Publication
Antwerp ,
Subject
Economics
Source (journal)
Journal of computational and applied mathematics. - Antwerp
Volume/pages
233(2010) :9 , p. 2213-2226
ISSN
0377-0427
ISI
000274605100010
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
A key problem in financial and actuarial research, and particularly in the field of risk management, is the choice of models so as to avoid systematic biases in the measurement of risk. An alternative consists of relaxing the assumption that the probability distribution is completely known, leading to interval estimates instead of point estimates. In the present contribution, we show how this is possible for the Value at Risk, by fixing only a small number of parameters of the underlying probability distribution. We start by deriving bounds on tail probabilities, and we show how a conversion leads to bounds for the Value at Risk. It will turn out that with a maximum of three given parameters, the best estimates are always realized in the case of a unimodal random variable for which two moments and the mode are given. It will also be shown that a lognormal model results in estimates for the Value at Risk that are much closer to the upper bound than to the lower bound.
E-info
https://repository.uantwerpen.be/docman/iruaauth/de683c/74d5c067ba6.pdf
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