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.

In the insurance literature, the Lundberg-Cramer model and Sparre-Anderson model have been discussed to a great extent. A general assumption is that the premium rate is constant over time. But such assumption does not reflect the randomness of the income procured.To describe the stochastic nature, later on many researchers have studied risk models with varying premium, with interest force etc. In this paper we consider the variability of income in two ways both positive and negative .we investigate risk model with random gain (positive jump) and claim amount(negative jump) under a renewal risk process with some assumptions. Explicit expressions for ruin/survival probability, severity of ruin, Barrier probability is also discussed.

Purpose -This paper considers a Sparre Andersen risk process for which the claims inter-arrival distribution is Generalized Exponential. The purpose of this paper is to find explicit expressions for the moments of time to ruin when a penalty is imposed at ruin. Design/methodology/approach -The study is focused on the function f d ðuÞ, the expected discounted penalty, which is due at ruin and may depend on the deficit at the time of ruin and also on the surplus prior to ruin. It shows that f d ðuÞ satisfies an integro-differential equation which is solved using Laplace transforms. Findings -The authors have chosen a penalty function, which is independent of the surplus immediately before ruin, and a closed form expression is obtained for f d ðuÞ, and then solved for the moments of time to ruin. Originality/value -New results are derived, many of which have mathematical and probabilistic interpretations, and additional insight is gained for the results in the renewal risk model.

In the renewal risk theory, the study of two sided jumps has been attracted by many researchers since its introduction. After the development of the distribution of modified inter time claim occurrence, the explicit expressions for ruin theory components in the literature under some assumptions, in this work, we examine probability density of the time of ruin, surplus immediately before ruin and deficit at ruin respectively under two sided risk process using some basic assumptions. Explicit expressions for distribution of interest are being derived.

We consider a renewal risk model in which the claim inter-arrival distribution is generalized exponential (GE). We obtain the probability distribution for the ladder height distribution and use it to find the bounds for the ultimate ruin probabilities for individual claim amount distributions. The method suggested by Dufresne and Gerber (1989) is used for finding the bounds for ruin probabilities.