BARRIER PROBABILITIES AND MAXIMUM SEVERITY OF RUIN FOR A RENEWAL RISK MODEL

In this paper, we consider a renewal risk model with dividend barrier, in which the claim inter-occurrence times are generalized exponential. We obtain explicit expression for the probability of absorption by an upper barrier b, before ruin occurs when the claim amount distribution is either mixed exponential or Gamma. We apply these results to obtain the distribution of the maximum deficit at the time of ruin. We also consider the numerical evaluation of the barrier probability, B(u, b), and the probability of maximum severity in some specific cases.