 
Summary: Finite time ruin probabilities
with one Laplace inversion
by
Florin Avram 1 and Miguel Usabel 2
Abstract In this work we present an explicit formula for the
Laplace transform in time of the nite time ruin probabilities of a
classical Levy model with phase{type claims. Our result generalizes
the ultimate ruin probability formula of Asmussen and Rolski(1991)
{see also the analog queueing formula for the stationary waiting time
of the M/Ph/1 queue in Neuts'(1981)){ and it considers the decit at
ruin as well.
1. Introduction
1. The model. We consider a classical risk process in continuous time fU t g t0
with Z k claim sizes and premium c per time unit,
U t = u + c t
N t
X
k=1
Z k (1.1)
where u are the initial reserves and N t the total number of claims up to time t. The
