Non-robustness with Respect to Intervention Costs in Optimal Control.

It is well known that a wide range of impulse control problems are continuous, but not differentiable, with respect to intervention cost as it approaches zero. We show a similar non-C¹ result, assuming that the problem and the value function are sufficiently regular. The result is that if the value function is locally C₁ in the state variable, then it does not admit first order approximation wrt. the intervention cost. Our analysis also covers problems with reflection (i.e., vanishing impulse). [ABSTRACT FROM AUTHOR]