Author(s)

Athena Makroglou

Abstract

An important problem of collective non-ruin is the estimation of the prob- abilities R(z,t) and R(z) of the finite and ultimate non-ruin respectively, where t is time and z is the initial reserve. The governing equations are first order Volterra integro-differential equations (VIDEs). Computational results for the finite time case are presented. These are obtained by using multiquadric approximation methods applied directly to the VIDE. Comparisons are made with results obtained by indirect approaches. 1 Introduction The problem of estimating the probability of non-ruin given an initial re- serve is very i

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