Computer treatment of the integro-differential equations of collective non-ruin; the finite time case Original Research Article

An important problem of collective non-ruin is the estimation of the probabilities R(z, t) and R(z) of the finite and ultimate non-ruin, respectively, where t is time and z the initial reserve. The governing equations are first-order Volterra integro-differential equations, partial (PVIDEs) in the finite time case and ordinary (VIDEs) in the ultimate non-ruin case, respectively.