On a perturbed Sparre Andersen risk model with dividend barrier and dependence

In this paper, we consider a Sparre Andersen risk model perturbed by a Brownian motion, where the inter-claim time and individual claim size follow some bivariate distribution. Assume that a barrier dividend strategy is applied to the surplus process, so that dividends are paid out whenever the surplus level attains a barrier bb. Integral equations and integro-differential equations satisfied by the Gerber–Shiu discounted penalty functions and the expected discounted dividend payments are derived, and solutions are also given for some special cases.