Long-Run Impulse Control with Generalized Discounting

Abstract

.In this paper, we investigate the effects of applying generalized (nonexponential) discounting on a long-run impulse control problem for a Feller–Markov process. We show that the optimal value of the discounted problem is the same as the optimal value of its undiscounted version. Next, we prove that an optimal strategy for the undiscounted discrete-time functional is also optimal for the discrete-time discounted criterion and nearly optimal for the continuous-time discounted one. This shows that the discounted problem, being time-inconsistent in nature, admits a time-consistent solution. Also, instead of a complex time-dependent Bellman equation, one may consider its simpler time-independent version.Keywordsimpulse controlaverage cost per unit timenonexponential discountinggeneralized discountingBellman equationMSC codes93E2049J2149K2160J25