It remained prevalent in the past years to obtain the precommitment strategies for Markowitz's mean-variance portfolio optimization problems, but not much is known about their time-consistent strategies. This paper takes a step to investigate the time-consistent Nash equilibrium strategies for a multiperiod mean-variance portfolio selection problem. Under the assumption that the risk aversion is, respectively, a constant and a function of current wealth level, we obtain the explicit expressions for the time-consistent Nash equilibrium strategy and the equilibrium value function. Many interesting properties of the time-consistent results are identified through numerical sensitivity analysis and by comparing them with the classical pre-commitment solutions.

This paper investigates a multi-period mean-variance portfolio selection with regime switching and uncertain exit time. The returns of assets all depend on the states of the stochastic market which are assumed to follow a discrete-time Markov chain. The authors derive the optimal strategy and the efficient frontier of the model in closed-form. Some results in the existing literature are obtained as special cases of our results.

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