The threshold dividend strategy on a class of dual model with tax payments

A class of dual risk model was considered in which dividends are paid under a threshold strategy and tax payments are paid according to a loss-carry forward system. For this model, the expectation of the discounted dividends until ruin was investigated and their corresponding integral equations, integro-differential equations and analytical expressions were derived. Finally, the case where profits follow an Erlang(2) distribution was solved.