Open-Loop Equilibrium Strategy for Mean-Variance Portfolio Problem Under Stochastic Volatility

26 Pages Posted: 27 Sep 2018 Last revised: 2 Feb 2019

See all articles by Tingjin Yan

Tingjin Yan

The Chinese University of Hong Kong (CUHK) - Department of Statistics

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics

Date Written: September 8, 2018

Abstract

We formulate the open-loop control framework for time-consistent mean-variance (TCMV) portfolio problems in incomplete markets with stochastic volatility (SV). We offer the existence and uniqueness results of the TCMV equilibrium controls for general SV models and derive explicit closed-form equilibrium controls for several popular models, including the Heston, Hull-White and 3/2 SV models. The uniqueness of the equilibrium controls are related to the mean-reverting speed of the volatility and the investment horizon.

Keywords: Mean-Variance Portfolio, Open-Loop Stochastic Control, Stochastic Volatility Model, Time Inconsistency

JEL Classification: C61, G11

Suggested Citation

Yan, Tingjin and Wong, Hoi Ying, Open-Loop Equilibrium Strategy for Mean-Variance Portfolio Problem Under Stochastic Volatility (September 8, 2018). Available at SSRN: https://ssrn.com/abstract=3246173 or http://dx.doi.org/10.2139/ssrn.3246173

Tingjin Yan

The Chinese University of Hong Kong (CUHK) - Department of Statistics ( email )

Shatin, N.T.
Hong Kong

Hoi Ying Wong (Contact Author)

The Chinese University of Hong Kong (CUHK) - Department of Statistics ( email )

Shatin, N.T.
Hong Kong

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