 
Summary: Convergence Rates in Approximating a Compound Distribution
John E. Angus
Abstract. In connection with the classical insurance risk problem,
Ross [1] develops a recursive formula for approximating a tail probability in a
geometrically compounded distribution. Here, we consider rates of convergence
for this approximation.
1. Background and Motivation
Ross [1] considered the following classical insurance risk problem. Claims are made
against an insurance company according to a homogeneous Poisson process with rate
> 0. The successive claim amounts are independent and identically distributed
(iid) non negative random variables Y1; Y2; ::: which are in turn independent of the
claim process. Claim amounts have common cumulative distribution function F
and ...nite mean ; 0 < < 1: The insurance company has initial capital x and
receives premiums and other income at a constant rate c > 0 per unit time. The ruin
probability is given by
p(x) = P
8
<
:
v(t)
