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.
Werner Hürlimann. "Conditional value-at-risk bounds for compound Poisson risks and a normal approximation." J. Appl. Math. 2003 (3) 141 - 153, 5 March 2003. https://doi.org/10.1155/S1110757X0320108X