Ruin Probabilities as Recurrence Sequences in a Discrete-Time Risk Process

Abstract The theory of linear recurrence sequences is applied to obtain an explicit formula for the ultimate ruin probability in a discrete-time risk process. It is assumed that the claims distribution is arbitrary but has finite support \0, 1, , m+1\ 0, 1, …, m + 1, for some integer m 1 m ≥ 1. The method requires finding the zeroes of an m degree polynomial and solving a system of m linear equations. An approximation is derived and some numerical results and plots are provided as examples.