Alternative approach to the optimality of the threshold strategy for spectrally negative Levy processes

Abstract

Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Lévy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. In this paper, we show that a threshold strategy (also called refraction strategy) forms an optimal strategy under the condition that the Lévy measure has a completely monotone density.