Improved bounds on tails of convolutions of compound distributions: Application to ruin probabilities for the risk process perturbed by diffusion.

In this paper we examine the convolution of a compound distribution with another given distribution. For this, new general upper and lower bounds on the tail probabilities of the convolution of a compound geometric distribution are derived. Also, such bounds are obtained under the truncated Cramér-Lundberg condition for the heavy-tailed case. Applications to the ruin probabilities of compound Poisson claims processes perturbed by diffusion as well as some new upper bounds are given. Also, several numerical examples to illustrate the effectiveness of the bounds are given. [ABSTRACT FROM AUTHOR]