Equilibrium dividend strategies in the dual model with a random time horizon

This paper investigates the dividend problem with non-exponential discounting in a dual model. We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable. Since the non-exponential discount function leads to a time inconsistent control problem, we study the equilibrium HJB-equation and give the associated verification theorem. For the case of a mixture of exponential discount functions and exponential gains, we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function. Besides, numerical examples are shown to illustrate our results.