Study of the Barrier Probability in a Classical Risk Model for two different claim amount distributions with same Mean

In this paper, we have considered a classical risk model with dividend barrier, in which claim inter-occurrence times are exponentially distributed. Our aim is to obtain explicit expression for the barrier probability B (u, b), the upper barrier being assumed to be 'b', before ruin occurs when the claim amount distribution is either exponential or erlangian. It is to be noted that the premium loading factor is taken to be 20% in both the cases. In order to ensure fair comparison we have chosen the exponential and erlangian parameters in such a way that their mean and hence the expected total claims is same for both the distributions over a given time interval. Ultimately through numerical evaluation of the barrier probability for both the claim amount distributions, we will investigate whether there is any significant difference between the two.