On the Sparre-Andersen dual model perturbed by diffusion

A diffusion perturbed Sparre-Andersen dual risk model was studied, in which the times between gains are independent and identically distributed random variables with a generalized Erlang(n) distribution. An integro-differential equation with certain boundary for the Laplace transform of the ruin time was derived and then its explicit expression was obtained. In particular, an explicit form of the Laplace transform of the time to ruin were studied when jump sizes were exponential. Finally, by studying the expected discounted dividends with the threshold-dividend strategy in the diffusion perturbed Sparre-Andersen dual risk model, an integro-differential equation with certain boundary for the expected discounted dividends was derived.