In this paper, we study the absolute ruin problems in a multi-layer compound Poisson model with constant interest force. The piecewise integro-differential equation for the Gerber-Shiu discounted penalty function is derived, and some explicit expressions are given when the claims are...

In this paper, we extend the compound binomial risk model to a Markov dependent model in which the claim occurrence and the claim amount are both regulated by a discrete time Markov process. The explicit expression for the "discounted" joint probability function of the surplus before ruin and...

In this paper, we consider a perturbed compound Poisson risk model with multi-layer dividend strategy. Integro-differential and integral equations for the expected discounted penalty function are derived and solved. When the claims are subexponentially distributed, the asymptotic formula for...

In this paper, we consider a Sparre-Andersen risk model with two-sided jumps, where the downward jumps represent the claims as usual and the upward jumps are also allowed to explain random gains. A generalized discounted penalty function is studied by using random walk techniques and the renewal...