J. Th. Runnenburg

Bounds on compound distributions and stop-loss premiums

Abstract In the actuarial literature a lot of attention is given to the approximation of aggregate claims distributions by compound Poisson and Polya distributions and their subsequent numerical evaluation. The present contribution derives bounds for the tail of compound distributions and stop-loss premiums. The bounds are obtained in an elementary manner based on a version of the Chebyshev inequality. The main point of this contribution consists in deriving bounds with explicit dependence on the distribution function itself as well as on some partial moments of it.