Time Consistent Behavior Portfolio Policy for Dynamic Mean-Variance Formulation

When we implement a portfolio selection methodology under a mean-risk formulation, it is essential to correctly model investors' risk aversion which may be time-dependent, or even state-dependent during the investment procedure. In this paper, we propose a behavior risk aversion model, which is a piecewise linear function of the current wealth level with a reference point at a preset investment target. Due to the time inconsistency of the resulting multi-period mean-variance model with an adaptive risk aversion, we investigate in this paper the time consistent behavior portfolio policy by solving a nested mean-variance game formulation. We derive semi-analytical time consistent behavior portfolio policy which takes a piecewise linear feedback form of the current wealth level with respect to the discounted investment target.