Mean-variance portfolio selection in jump-diffusion model under no-shorting constraint: A viscosity solution approach
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.
Cite
@article{arxiv.2406.03709,
title = {Mean-variance portfolio selection in jump-diffusion model under no-shorting constraint: A viscosity solution approach},
author = {Xiaomin Shi and Zuo Quan Xu},
journal= {arXiv preprint arXiv:2406.03709},
year = {2024}
}