Mean–variance portfolio selection under a non-Markovian regime-switching model

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 a Markov chain, we obtain both the optimal strategy and the efficient frontier in explicit forms. In particular, we revisit the Markovian regime-switching model in which the coefficients are deterministic functions of the Markov chain.