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

Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy 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. Kyprianou, Loeffen and Perez [28] have shown that a refraction strategy (also called threshold strategy) forms an optimal strategy under the condition that the Levy measure has a completely monotone density. In this paper, we propose an alternative approach to this optimal problem.Comment: 16 page

The first exit time and ruin time for a risk process with reserve-dependent income

This paper investigates the first exit time and the ruin time of a risk reserve process with reserve-dependent income under the assumption that the claims arrive as a Poisson process. We show that the Laplace transform of the distribution of the first exit time from an interval satisfies an integro-differential equation. The exact solution for the classical model and for the Embrechts-Schmidli model are derived.First exit time Ruin time Ruin probability Risk reserve process Embrechts-Schmidli model