Dividend Problem With Parisian Delay For The Classical Risk Model With Debit Interest

The idea of Parisian implementation delay originates from the concept of Parisian op-tions.Considering the time lag between the decision to pay dividends and its implementation,Chesney et al.(1997)raised the question about the dividends with Parisian delay.The implementation to pay dividends is taken when the surplus keeps staying above the barrier and lasts over the time lag d.The size of dividends equals to the overflow above the barrier and the decision is revoked if the process dips below the barrier during the interval.Dassios and Wu(2009)studied the problem of Parisian implementation delay dividends in a classical risk model in the way of excursion and obtained an optimal barrier.As an extnetion of Dassios and Wu's paper,we study in this situation:we segment the excursion from the first time to reach the dividend barrier to the first time to dividend by the same means.We get another representation of this excursion,then we get the expression of the aggregate dividends.In this paper,we also consider a.situation that the time lag is a.random variable.Suppose that the time lag has an Erlang(2)distribution in the classical risk model.we get the aggregate dividends by the same mean and an optimal barrier.