The numerical calculation ofU(w, t), the probability of non-ruin in an interval (0,t)

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Abstract
A formula for U(w, t), the distribution function of the waiting time of a potential customer who joins a queue with a single server at epoch t after service commences without a queue was derived for dam theory by Gani & Prabhu (1959) and for queues by Beneš (1960). Here we use it to calculate numerically the probability of non-ruin in risk theory with an assumption that X(t), the accumulated claims during the interval (0, t), is a stochastic process with independent increments occurring at the event points of a stationary process. The difficulties encountered are described in some detail and suggestions made for the attainment of three-decimal accuracy in U(w, t).