Recursive Methods for Computing Finite Time Ruin Probabilities for Phase-Distributed Claim Sizes

Finite time ruin methods typically rely on diffusion approximations or discrimination. We propose a new method by looking at the surplus process embedded at claim instants and develop a recursive scheme for calculating ruin probabilities. It is assumed that claim sizes follow a phase-type distribution. The proposed method is exact. The application of the method reveals where in the future the relative vulnerability to the company lies. KEYWORDS Finite-time ruin probability; Recursive methods; Phase-type distributions; Risk theory