On a perturbed Sparre Andersen risk model with threshold dividend strategy and dependence

In this paper, we consider a Sparre Andersen risk model perturbed by a Brownian motion, where the individual claim sizes are dependent on the interclaim times. We assume that dividends are paid off under a threshold strategy. Integral and integro-differential equations satisfied by the Gerber-Shiu functions are obtained, and a solution procedure is also proposed.