  In this paper, we consider a continuous-time mean-variance portfolio
selection with regime-switching and random horizon. Unlike previous works, the
dynamic of assets are described by non-Markovian regime-switching models in the
sense that all the market parameters are predictable with respect to the
filtration generated jointly by Markov chain and Brownian motion. We formulate
this problem as a constrained stochastic linear-quadratic optimal control
problem. The Markov chain is assumed to be independent of the Brownian motion.
So the market is incomplete. We derive closed-form expressions for both the
optimal portfolios and the efficient frontier. All the results are different
from those in the problem with fixed time horizon.
