Continuous-time mean-variance portfolio selection with no-shorting constraints and regime-switching

Ping Chen,Haixiang Yao

doi:10.3934/jimo.2018166

Abstract

The present article investigates a continuous-time mean-variance portfolio selection problem with regime-switching under the constraint of no-shorting. The literature along this line is essentially dominated by the Hamilton-Jacobi-Bellman (HJB) equation approach. However, in the presence of switching regimes, a system of HJB equations rather than a single equation need to be tackled concurrently, which might not be solvable in terms of classical solutions, or even not in the weaker viscosity sense as well. Instead, we first introduce a general result on the sign of geometric Brownian motion with jumps, then derive the efficient portfolio and frontier via the maximum principle approach; in particular, we observe, under a mild technical assumption on the initial conditions, that the no-shorting constraint will consistently be satisfied over the whole finite time horizon. Further numerical illustrations will be provided.

Highlights

Mean-variance portfolio selection is pioneered by Markowitz in 1952 (see Markowitz (1952))
Our present work considers a continuous-time optimal mean-variance portfolio selection problem over the regime-switching setting, or Makov-modulated models
This paper is an extension of the continuous-time mean-variance portfolio selection model proposed by Zhou and Yin (2003)

Summary

Introduction

Mean-variance portfolio selection is pioneered by Markowitz in 1952 (see Markowitz (1952)). The main idea is to find the optimal portfolio weights among assets to achieve the optimal trade-off between the mean and the variance of the portfolio return. Thereafter, Markowitz’s work was extended in various aspects. Samuelson (1969) extended the work of Markowitz to a dynamic model and considered a discrete-time consumption-investment model with the objective of maximizing the overall expected consumption. Merton (1969, 1971) adapted a continuous time stochastic optimal control to model and obtain the optimal portfolio strategy which results in the two-fund separation theorem. Li and Ng (2000) extended Markowitz’s model to a discrete dynamic setting, and both the optimal strategy and the efficient frontier were obtained explicitly. No-shorting constraint, regime-switching, mean-variance, efficient frontier, Riccati equation.

PING CHEN AND HAIXIANG YAO

Hilbert space

Then we have

Conclusion

Minerva Access is the Institutional Repository of The University of Melbourne