Dividend Problems for Finite Time Interval in the Classical Risk Model

In this paper, we study the dividend problems for finite time interval in the classical risk model. Assume that the dividends are paid according to a barrier strategy in the time interval 0,t, i.e., given a nonnegative barrier value b, the dividends only can be paid when the surplus exceeds b and the excess is paid as dividend. Applying the ``differential argument'', the equation for the total expected discounted dividends in the time interval 0,t (V(x;t)) is derived, and the explicit expression for the Laplace transform of V(x;t) with respect to t is obtained under the assumption that the claim sizes are exponentially distributed. Finally, a numerical example is given by Stehfest method.