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doi: 10.3934/jimo.2019133

## 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

Received  March 2019 Revised  July 2019 Published  October 2019

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.

Citation: Jiannan Zhang, Ping Chen, Zhuo Jin, Shuanming Li. Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019133
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