How to estimate the value at risk under incomplete information
How to estimate the value at risk under incomplete information
Faculty of Applied Economics

article

2010
Antwerp
, 2010

Economics

Journal of computational and applied mathematics. - Antwerp

233(2010)
:9
, p. 2213-2226

0377-0427

000274605100010

E

English (eng)

University of Antwerp

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.

https://repository.uantwerpen.be/docman/iruaauth/de683c/74d5c067ba6.pdf

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