Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model

Jiannan Zhang; Ping Chen; Zhuo Jin; Shuanming Li

doi:10.3934/jimo.2019133

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2021, Volume 17, Issue 2: 765-777. Doi: 10.3934/jimo.2019133

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Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model

Centre for Actuarial Studies, Department of Economics, The University of Melbourne, VIC, 3010, Australia

^* Corresponding author: Ping Chen
^* Corresponding author: Ping Chen

Received: February 28, 2019

Revised: June 30, 2019

Early access: October 2019

Published: March 2021

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Abstract

This paper investigates a continuous-time mean-variance portfolio selection problem based on a log-return model. The financial market is composed of one risk-free asset and multiple risky assets whose prices are modelled by geometric Brownian motions. We derive a sufficient condition for open-loop equilibrium strategies via forward backward stochastic differential equations (FBSDEs). An equilibrium strategy is derived by solving the system. To illustrate our result, we consider a special case where the interest rate process is described by the Vasicek model. In this case, we also derive the closed-loop equilibrium strategy through the dynamic programming approach.

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Mathematics Subject Classification: Primary: 90B50, 93E20; Secondary: 91G80.

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