On the formulation of a stochastic model for an accumulated claim amount under renewal risk process

Abstract

Traditionally an Insurance risk process is characterised by claim process using a renewal process assuming claim amount is independent of inter claim time. It is usually modelled as a stochastic process such as Compound Poisson Process. It is also assumed that the premium amount is proportional to the time we refer with each claim. Depending upon the type of portfolio, the insurer can make a variety of different assumptions on the sequence of inter occurrence times and accumulated claim amount as well. In this paper we discuss a stochastic model for Renewal Risk model with different distributions to number of demands and Generalised Exponential distribution to the impact of each demand under the insurance claim scenario. Assume that number of cases is independent of the severity of each case throughout the model. We present the model when case frequency is Poison or Negative Binomial or Geometric and also present severity of each case with Generalised Exponential distribution.