A Lévy Risk Model with Ratcheting Dividend Strategy and Historic High-Related Stopping

Abstract

This paper focuses on the De Finetti’s dividend problem for the spectrally negative Lévy risk process, where the dividend is deducted from the surplus process according to the racheting dividend strategy which was firstly introduced in Albrecher et al. (2018). A major feature of the racheting strategy lies in which the dividend rate never decreases. Unlike the conventional studies, the closed form expression for the expected, accumulated, and discounted dividend payments until the draw-down time (rather than the ruin time) is obtained in terms of the scale functions corresponding to the underlying Lévy process. The optimal barrier for the ratcheting strategy is also studied, where the dividend rate can be increased. Finally, two special cases, where the scale functions are explicitly known, i.e., the Brownian motion with drift and the compound Poisson model, are considered to illustrate the main result.

A Lévy risk model with ratcheting and barrier dividend strategies

“…We believe that the ratcheting strategy represents another subclass of constrained dividend strategies (other than the threshold dividend strategies) that is comparatively more acceptable in the community of practitioners. After that, there are some recent papers on ratcheting dividend strategy for different risk models, such as Albrecher et al [1], Albrecher et al [2], Zhang and Liu [20] and Song and Sun [15].…”