The expected discounted penalty function under the compound Poisson risk model with tax payments and a threshold dividend strategy

The compound Poisson risk model was considered in which taxes were paid according to a loss-carry forward system and dividends were paid under a threshold strategy. For this model, the ruin quantities were discussed by defining an expected discounted penalty function at ruin and the analytical integro-differential equation satisfied by the expected discounted penalty function was derived. Finally, in the case where the individual claims follow an exponential distribution, explicit expressions for the ruin probability were given.