  In this paper, we investigate the effects of applying generalised
(non-exponential) 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.
