Explicit solutions for continuous time mean-variance portfolio selection with nonlinear wealth equations

TL;DR

This paper derives explicit solutions for a continuous-time mean-variance portfolio problem with a nonlinear wealth equation, providing explicit strategies and frontiers, and demonstrating the model's applicability to key cases.

Contribution

It introduces an explicit viscosity solution to the HJB equation for a nonlinear wealth model, enabling explicit portfolio strategies and frontier analysis.

Findings

Explicit viscosity solution to the HJB equation obtained

Explicit efficient portfolio strategy derived

Model covers three important special cases

Abstract

This paper concerns the continuous time mean-variance portfolio selection problem with a special nonlinear wealth equation. This nonlinear wealth equation has a nonsmooth coefficient and the dual method developed in [6] does not work. We invoke the HJB equation of this problem and give an explicit viscosity solution of the HJB equation. Furthermore, via this explicit viscosity solution, we obtain explicitly the efficient portfolio strategy and efficient frontier for this problem. Finally, we show that our nonlinear wealth equation can cover three important cases.