Optimal dividend problem for a generalized compound Poisson risk model

摘要

In this note we study the optimal dividend problem for a company whosesurplus process, in the absence of dividend payments, evolves as a generalizedcompound Poisson model in which the counting process is a generalized Poissonprocess. This model including the classical risk model and the Polya-Aepplirisk model as special cases. The objective is to find a dividend policy so asto maximize the expected discounted value of dividends which are paid to theshareholders until the company is ruined. We show that under some conditionsthe optimal dividend strategy is formed by a barrier strategy.