The Expected Discounted Penalty Function in the Generalized Erlang (n) Risk Model with Two-Sided Jumps and a Constant Dividend Barrier

In this paper, the generalized Erlang(n) risk model with two-sided jumps and a constant dividend barrier is considered. We assume that the downward jump sizes follow an arbitrary distribution and the upward jump sizes follow the mixed Erlang distribution. An integro-differential equation with boundary conditions for the expected discounted penalty function is derived and the solution is provided. The defective renewal equation for the expected discounted penalty function with no barrier is derived. We also give an example to obtain the expression of the expected discounted penalty function when the claim amounts are exponentially distributed.