Burr Distribution as an Actuarial Risk Model and the Computation of Some of Its Actuarial Quantities Related to the Probability of Ruin

Abstract

In this paper, we have used an algorithm to fit the Burr XII distribution to a set of insurance data. As it is well known, the probability of ultimate ruin is obtained as a solution to an integro-differential equation and in case, the claim severity is distributed as Burr XII distribution, this equation has to be solved numerically to obtain an approximation to the probability of ultimate ruin. Two numerical algorithms, namely the stable recursive algorithm and the method of product integration have been used to obtain numerically an approximation to this probability of ultimate ruin. The use of these two numerical algorithms provides a scope for comparing the consistency in values obtained by them. The first two moments of the time to ruin in case of Burr XII distributed claim severity have also been computed using the probability of ultimate ruin obtained through the stable recursive algorithm as an input. All these computations have been done under the assumption of the classical risk model.