2022/05/13 by Chen, Tian, Liu, Ruyi, Wu, Zhen
#05B05 #05B25 #20B25 #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2205.06434
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.