Journal of Applied Mathematics
Volume 2003 (2003), Issue 3, Pages 141-153

Conditional value-at-risk bounds for compound Poisson risks and a normal approximation

Werner Hürlimann

Schönholzweg 24, Winterthur CH-8409, Switzerland

Received 16 January 2002; Revised 22 September 2002

Copyright © 2003 Werner Hürlimann. 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.


A considerable number of equivalent formulas defining conditional value-at-risk and expected shortfall are gathered together. Then we present a simple method to bound the conditional value-at-risk of compound Poisson loss distributions under incomplete information about its severity distribution, which is assumed to have a known finite range, mean, and variance. This important class of nonnormal loss distributions finds applications in actuarial science, where it is able to model the aggregate claims of an insurance-risk business.