Smooth Fit Principle for Impulse Control of Multidimensional Diffusion Processes

Value functions of impulse control problems are known to satisfy Quasi-Variational Inequalities (QVI) (Bensoussan and Lions (1982)). This paper proves the smooth-fit C1 property of the value function for multi-dimensional controlled diffusions, using a viscosity solution approach. We show by examples how to exploit this regularity property to derive explicitly optimal policy and value function. ∗Department of Industrial Engineering and Operations Research, University of California at Berkeley, CA 94720-1777. Email address: [email protected] †Department of Mathematics, University of California at Berkeley, CA 94720-3840. Email address: [email protected]