Journal of Applied Mathematics
Volume 2003 (2003), Issue 3, Pages 141-153
doi:10.1155/S1110757X0320108X
Abstract
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.