Continuous-time Markowitz's model with constraints on wealth and portfolio

Abstract

We consider a continuous-time Markowitz's model with bankruptcy prohibition and convex cone portfolio constraints. We first transform the problem into an equivalent one with bankruptcy prohibition but without portfolio constraints. The latter is then treated by martingale theory. This approach allows one to directly present the semi-analytical expressions of the pre-committed efficient policy without using the viscosity solution technique but within the framework of cone portfolio constraints. The numerical simulation also sheds light on results established in this paper.