In this paper we consider a Markov-modulated dual risk reserve process with a multi-threshold dividend strategy. We study the risk reserve process that can start at any level of the threshold. An integral equation for the conditional non-ruin probability is obtained. Further in two states, we...

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....

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...