Approximating Impulse Control by Iterated Optimal Stopping

Abstract

In general it is not possible to reduce impulse control to optimal stopping, because the choice of the first intervention time $\tau _1$ and the first impulse $\zeta _1$ will influence the next and so on. However, if we allow only (up to) a fixed finite number n of interventions, then the corresponding impulse control problem can be solved by solving iteratively n optimal stopping problems.