| This dissertation shows that the value function for the impulse control of multidimensional diffusions is the unique viscosity solution of the associated HJB equation under certain conditions. By studying this HJB equation, we prove that its solution (i.e., the value function) belongs to the Sobolev space W2,p for all p < infinity, from which the smooth fit C 1 property of the value function follows directly. As an application of the smooth-fit principle, we then study the classical cash management problem (Constantinides and Richard, 1978) and derive the explicit structure of the value function as well as the optimal policy.;Finally, we establish similar results for the case when the underlying process is a multidimensional jump diffusion, in which case the HJB equation becomes a partial integro-differential equation, by exploiting properties of the Levy type integral operators. |
