Continuous-Time Mean-Variance Portfolio Selection with Bankruptcy Prohibition

Abstract

A continuous-time Markowitz's mean-variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible portfolio is not allowed to be below zero at any time. The feasibility of the problem is first characterized. Then, after having solved a system of algebraic equations, minimum variance portfolios are derived as the replicating portfolios of some contingent claims, and the minimum variance frontier is obtained. In the special case where the market coefficients are deterministic, more explicit results are obtained.