Modeling of Claim Severity through the Mixture of Exponential Distribution and Computation of its Probability of Ultimate Ruin

Abstract

In this paper we have discussed the infinite time ruin probabilities in continuous time in a compound Poisson process with a constant premium rate for the mixture of exponential claims. Firstly, we  have fitted the mixture of two exponential and the mixture of three exponential to a set of claim data and thereafter, have computed the probability of ultimate ruin through a method giving its exact expression and then through a numerical method, namely the method of product integration.  The derivation of the exact expression for ultimate ruin probability for the mixture of three and mixture of two exponential is done through the moment generating function of the maximal aggregate loss random variable. Consistencies are observed in the values of ultimate ruin probabilities obtained by both the methods.