The Erlang (2) Renewal Risk Model With Tax

Risk theory is a focus of actuarial, insurance and mathematics, it has developed promptly in recent ten years.Ruin theory is the keystone of risk theory.In this paper, the classical Cramer-Lundberg risk model and Erlang (2) renewal risk model are considered in essence, the barrier strategies are discusses based on the above two models.The most novel strategy, which is the so-calles tax, is investigated.In this paper, first we introduce the classical Cramer-Lundberg risk model and Erlang (2) renewal risk model, then present various extend of risk model and related conclusions. At last, we generalize the classical Cramer-Lundberg risk model with tax to Erlang (2) renewal risk model with tax.The integro-differential equations between the ruin probabilty and Gerber-Shiu discounted penalty function in the Erlang (2) risk model with and without tax are obtained, respectively.