On optimal joint reflective and refractive dividend strategies in spectrally positive Levy models

Abstract

The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this context, numerous papers considered threshold (refractive) and barrier (reflective) dividend strategies. These were shown to be optimal in a number of different contexts for bounded and unbounded payout rates, respectively. In this paper, motivated by the behavior of some dividend paying stock exchange companies, we determine the optimal dividend strategy when both continuous (refractive) and lump sum (reflective) dividends can be paid at any time, and if they are subject to different transaction rates. We consider the general family of spectrally positive Lévy processes. Us..