The Penalty Function Of Sparre Andersen Model With A Threshold Dividend Strategy

In this paper,we consider a Sparre Andersen risk model with a dividend barrier. The complete dividend notion proposed by Shuanming Li and Jose Garrido, with the assumption that the surplus is above b is extended to the situation of dividend by proportion. Then we discussed the boundary condition which the expected discounted penalty function satisfies,when claim waiting times are generalized Elang(n) distributed(i.e., convolution of n exponential distributions with possibly different parameters).Moreover, we give the integro-differential equation which the expected discounted penalty function satisfied.This paper includes four chapters. In the first chapter, the relative background on this paper is given. The preparatory knowledge underlying this paper and the model we consider in this paper are introduced in the second one. The third chapter is the main body of this paper, in which the expected discounted penalty function of a Sparre Andersen risk model with a threshold dividend barrier is considered,and shown that the expected discounted penalty function satisfies a certain integro-differential equation. In the last chapter ,the main results of this paper are given.