Calculating Ruin Probabilities via Product Integration

Simple approximations of ruin probabilities

A “simple approximation” of a ruin probability is an approximation using only some moments of the claim distribution and not the detailed tail behaviour of that distribution. Such approximations may be based on limit theorems or on more or less ad hoc arguments. The most successful simple approximation is certainly the De Vylder approximation, which is based on the idea to replace the risk proc...

Ruin Probabilities for Erlang(2) Risk Processes1

In this paper we consider a risk process in which claim inter-arrival times have an Erlang(2) distribution. We consider the in…nite time survival probability as a compound geometric random variable and give expressions from which both the survival probability from initial surplus zero and the ladder height distribution can be calculated. We consider explicit solutions for the survival/ruin prob...

Finite Time Ruin Probabilities and Martingales

In this paper we give an introduction to collective risk theory in its simplest form. Our aims are to indicate how some basic facts may be obtained by martingale methods and to point out some open problems

Ruin probabilities for competing claim processes ∗

Let C1, C2, . . . , Cm be independent subordinators with finite expectations and denote their sum by C. Consider the classical risk process X(t) = x+ct−C(t). The ruin probability is given by the well known Pollaczek-Hinchin formula. If ruin occurs, however, it will be caused by a jump of one of the subordinators whose sum constitutes C. Formulae for the probability that ruin is caused by Ci are...

Exact Ruin Probabilities for Lévy Processes