Mean-variance portfolio selection in jump-diffusion model under no-shorting constraint: A viscosity solution approach

TL;DR

This paper develops a viscosity solution approach to solve a constrained mean-variance portfolio selection problem in a jump-diffusion model, providing explicit optimal controls and closed-form solutions.

Contribution

It introduces a novel viscosity solution method for the constrained MV problem under jump-diffusion dynamics, correcting previous literature flaws.

Findings

Explicit viscosity solution for the Hamilton-Jacobi-Bellman equation

Closed-form expressions for efficient portfolios and frontiers

Examples demonstrating decoupled ODE cases

Abstract

This paper concerns a continuous time mean-variance (MV) portfolio selection problem in a jump-diffusion financial model with no-shorting trading constraint. The problem is reduced to two subproblems: solving a stochastic linear-quadratic (LQ) control problem under control constraint, and finding a maximal point of a real function. Based on a two-dimensional fully coupled ordinary differential equation (ODE), we construct an explicit viscosity solution to the Hamilton-Jacobi-Bellman equation of the constrained LQ problem. Together with the Meyer-It\^o formula and a verification procedure, we obtain the optimal feedback controls of the constrained LQ problem and the original MV problem, which corrects the flawed results in some existing literatures. In addition, closed-form efficient portfolio and efficient frontier are derived. In the end, we present several examples where the two-dimensional ODE is decoupled.