In this paper, we study the dual risk process in ruin theory (see e.g. Cramér, H. 1955. Collective Risk Theory: A Survey of the Theory from the Point of View of the Theory of Stochastic Processes. Ab Nordiska Bokhandeln, Stockholm, Takacs, L. 1967. Combinatorial methods in the Theory of...

In this paper we consider a multi-threshold compound Poisson risk model. A piecewise integro-differential equation is derived for the Gerber-Shiu discounted penalty function. We then provide a recursive approach to obtain general solutions to the integro-differential equation and its...

The expected discounted penalty function proposed in the seminal paper by Gerber and Shiu [Gerber, H.U., Shiu, E.S.W., 1998. On the time value of ruin. North Amer. Actuarial J. 2 (1), 48-78] has been widely used to analyze the joint distribution of the time of ruin, the surplus immediately...

In this paper, we extend the Cramér-Lundberg insurance risk model perturbed by diffusion to incorporate stochastic volatility and study the resulting Gerber-Shiu expected discounted penalty (EDP) function. Under the assumption that volatility is driven by an underlying Ornstein-Uhlenbeck (OU)...

In this paper, we generalize the Cramér-Lundberg risk model perturbed by diffusion to incorporate jumps due to surplus fluctuation and to relax the positive loading condition. Assuming that the surplus process has exponential upward and arbitrary downward jumps, we analyze the expected...