  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.
