Continuous-Time Mean-Variance Portfolio Selection with Constraints on Wealth and Portfolio

TL;DR

This paper addresses continuous-time mean-variance portfolio optimization with wealth and portfolio constraints, providing semi-analytical solutions and practical insights through theoretical transformation and numerical simulations.

Contribution

It transforms a complex constrained problem into an unconstrained one and derives semi-analytical solutions without viscosity methods, advancing the theoretical framework.

Findings

Semi-analytical expressions for optimal policies are obtained.

The approach simplifies solving constrained mean-variance problems.

Numerical simulations validate the theoretical results.

Abstract

We consider continuous-time mean-variance portfolio selection with bankruptcy prohibition under convex cone portfolio constraints. This is a long-standing and difficult problem not only because of its theoretical significance, but also for its practical importance. First of all, we transform the above problem into an equivalent mean-variance problem with bankruptcy prohibition without portfolio constraints. The latter is then treated using martingale theory. Our findings indicate that we can directly present the semi-analytical expressions of the pre-committed efficient mean-variance policy without a viscosity solution technique but within a general framework of the cone portfolio constraints. The numerical simulation also sheds light on results established in this paper.