This paper aims to find the time-consistent equilibrium strategy for a mean-variance portfolio
selection problem under a non-Markovian regime-switching model, in which the coefficients
are adapted to the filtration generated by a Markov chain. By introducing and investigating
systems of coupled backward stochastic differential equations driven by the Markov chain,
we obtain feedback representations of both open-loop equilibrium strategies and linear
closed-loop equilibrium strategies. We also make further comparisons with the existing …

In this paper, we investigate the mean–variance portfolio selection problem in a continuous-
time setting. We assume that the coefficients in the model are random and adapted to the
filtration generated by a Markov chain. Instead of using the embedding approach which is
widely adopted in the existing literature, we study the problem from the viewpoint of mean-
field formulation and provide a distinctive and straightforward approach. By introducing and
discussing a new system of mean-field backward stochastic differential equations driven by …