TALK by B. Øksendal
### June 4, 2008

### Optimal stochastic impulse control with delayed reaction

#### Bernt Øksendal (University of Oslo)

We study impulse control problems of jump diffusions with delayed
reaction. This means that there is a delay δ > 0 between the
time when a decision for intervention is taken and the time when the
intervention is actually carried out.
We show that under certain conditions this problem can be transformed
into a sequence of iterated no-delay optimal stopping problems and
there is an explicit relation between the solutions of these two
problems.
The results are illustrated by an example where the problem is to
find the optimal times to increase the production capacity of a firm,
assuming that there are transaction costs with each new order and the
increase takes place δ time units after the (irreversible)
order has been placed.
The presentation is based on joint work with Agnès Sulem: "Optimal
stochastic control with delayed reaction", Applied Mathematics and
Optimization (to appear).