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On A Multi-Dimensional Singular Stochastic Control Problem: The Parabolic Case, Nhat Do Minh Nguyen

Wayne State University Dissertations

This dissertation considers a stochastic dynamic system which is governed by a multidimensional diffusion process with time dependent coefficients. The control acts additively on the state of the system. The objective is to minimize the expected cumulative cost associated with the position of the system and the amount of control exerted. It is proved that Hamilton-Jacobi-Bellman’s equation of the problem has a solution, which corresponds to the optimal cost of the problem. We also investigate the smoothness of the free boundary arising from the problem.

In the second part of the dissertation, we study the backward parabolic problem for a …