A REMARK ON THE MOMENTS OF RUIN TIME IN CLASSICAL RISK THEORY

We prove that the pth moment of the ruin time in a classical risk process exists if and only if the (p+1)th moment of the claim size exists. The proof uses a theorem of Erdös on the speed of convergence in the law of large numbers. The result can also be obtained using fractional derivatives in Laplace transforms. Our proof is computational and again it shows the link between the limit behaviour in the (continuous time) compound Poisson process and the usual (discrete time) limit theorems in probability theory. © 1990.