Unified Framework of Mean-Field Formulations for Optimal Multi-Period Mean-Variance Portfolio Selection

Accepted by IEEE Transactions on Automatic Control, Forthcoming

29 Pages Posted: 11 Apr 2014 Last revised: 19 Apr 2020

See all articles by Xiangyu Cui

Xiangyu Cui

Shanghai University of Finance and Economics - School of Statistics and Management

Xun Li

Hong Kong Polytechnic University

Duan Li

Chinese University of Hong Kong; City University of Hong Kong

Date Written: February 21, 2014

Abstract

When a dynamic optimization problem is not decomposable by a stage-wise backward recursion, it is nonseparable in the sense of dynamic programming. The classical dynamic programming-based optimal stochastic control methods would fail in such nonseparable situations as the principle of optimality no longer applies. Among these notorious nonseparable problems, the dynamic mean-variance portfolio selection formulation had posed a great challenge to our research community until recently. Different from the existing literature that invokes embedding schemes and auxiliary parametric formulations to solve the dynamic mean-variance portfolio selection formulation, we propose in this paper a novel mean-field framework that offers a more efficient modeling tool and a more accurate solution scheme in tackling directly the issue of nonseparability and deriving the optimal policies analytically for the multi-period mean-variance-type portfolio selection problems.

Keywords: Stochastic optimal control, mean-field formulation, multi-period portfolio selection, multi-period mean-variance formulation, intertemporal restrictions, risk control over bankruptcy

JEL Classification: G11

Suggested Citation

Cui, Xiangyu and Li, Xun and Li, Duan and Li, Duan, Unified Framework of Mean-Field Formulations for Optimal Multi-Period Mean-Variance Portfolio Selection (February 21, 2014). Accepted by IEEE Transactions on Automatic Control, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2410682 or http://dx.doi.org/10.2139/ssrn.2410682

Xiangyu Cui (Contact Author)

Shanghai University of Finance and Economics - School of Statistics and Management ( email )

777 Guoding Road
Shanghai, Shanghai 200433
China

Xun Li

Hong Kong Polytechnic University ( email )

The Hong Kong Polytechnic University
Hung Hom, Kowloon
Hong Kong

Duan Li

City University of Hong Kong

Tat Chee Avenue
Kowloon Tong
Kowloon
Hong Kong
852 3442 8591 (Phone)

Chinese University of Hong Kong ( email )

Shatin, New Territories
Hong Kong

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