COMPUTATIONAL METHODS IN RISK THEORY - A MATRIX-ALGORITHMIC APPROACH

This paper is concerned with the numerical computation of the probability psi(u) of ruin with initial reserve u. The basic assumption states that the claim size distribution is phase-type in the sense of Neuts. The models considered are: the classical compound Poisson risk process, the Sparre Anderse process and varying environments which are either governed by a Markov process or exhibit periodic fluctuations. The computational steps involve the iterative solution of a non-linear matrix equation Q = psi(Q) as well as the evaluation of matrix-exponentials e(Qu). A number of worked-out numerical examples are presented.