Ruin probabilities as recurrence sequences in a discrete-time risk process
Abstract
We apply the theory of linear recurrence sequences to find an expression for the ultimate ruin probability in a discrete-time risk process. We assume the claims follow an arbitrary distribution with support \0,1,…,m\, for some integer m2. The method requires to find the zeroes of an m degree polynomial and to solve a system of m linear equations. An approximation is derived from the exact ruin formula and several numerical results and plots are provided as examples.
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