Discrete-Time Behavioral Portfolio Selection Under Prospect Theory

Abstract

We formulate and study a general multi-period behavioral portfolio selection model under Kahneman and Tversky's prospect theory, featuring an incomplete market and an S-shaped utility function. We first discuss the ill-posedness issue under a multi-period framework and identify the conditions for the well-posedness under which infinitely leveraging an asset is not optimal for the investor. Moreover, we show that the well-posedness of the multi-period portfolio selection problem can be characterized in terms of an induced loss-aversion measure, which is an increasing function of time. Under the conditions for well-posedness, we solve the multi-period behavioral portfolio selection problem completely by deriving its semi-analytical optimal policy. In particular, we identify two cases: the case with one risky asset and the case with multiple risky assets that are jointly elliptically distributed, under which the optimal behavioral portfolio policy takes a piecewise linear feedback form. For the multiple risky assets case, we further demonstrate that the two-fund separation is still valid under the S-shaped utility. We also discuss the implications of our findings to the well documented phenomena of non-participation effect and horizon effect.