Abstract

Consider a state process X as a standard Brownian motion x+W(.) started at x \in R. We discuss the finite-fuel impulse control problem of optimally tracking this process by an adapted process of bounded total variation, so as to minimize the total expected discounted cost. The performance criterion reflects both a fixed cost and a cost proportional to the impulse's size that are incurred when controller deploys an impulse to reposition the system's state. The criterion also incurs costs proportional to the amount of fuel being used and to the quadratic deviation from the origin(both up to, and at, termination). We solve the resulting optimization problem and we provide an explicit characterization of an optimal control strategy under general assumptions.
 

Convenor:Aidan Sudbury