The self-coordination mean-variance strategy in continuous time

¹ School of Statistics and Academy of Statistics and Interdisciplinary Sciences, East China Normal University, Shanghai, P.R. China
² School of Data Science, City University of Hong Kong, Hong Kong, P.R. China
³ School of Statistics and Management, Dishui Lake Advanced Finance Institute, Shanghai University of Finance and Economics, Shanghai, P.R. China

^* Corresponding author: cui.xiangyu@mail.shufe.edu.cn

Received: 20 April 2022
Accepted: 11 October 2023

Abstract

The dynamic mean-variance portfolio selection problem is time inconsistent. In the literature, scholars try to derive the pre-committed strategy, the time consistent strategy and the self-coordination strategy. The pre-committed strategy only concern the global investment interest of the investor. The time consistent strategy only concerns the local investment interests of the investor, while the self-coordination strategy balances between the global investment interest and local investment interests of the investor. However, the self-coordination strategy is only studied for the discrete time mean-variance setting. We study the self-coordination strategy for the continuous time mean-variance setting in this paper. With the help of mean-field reformulation, we derive the analytical self-coordination mean-variance strategy and show that the pre-committed strategy and time consistent strategy are special cases of the self-coordination strategy.