Optimal consumption and portfolio selection problems under loss aversion with downside consumption constraints

This paper investigates continuous-time optimal portfolio and consumption problems under loss aversion in an infinite horizon. The investor's goal is to choose optimal portfolio and consumption policies to maximize total discounted S-shaped utility from consumption. The consumption rate process is subject to a downside constraint. The optimal consumption and portfolio policies are obtained through the martingale method and replication technique. Numerical results indicate the differences between the loss averse investor and the constant relative risk averse (CRRA) investor on the optimal consumption and portfolio policies: the loss averse investor likes consuming more money but exposing less to risk than that of the CRRA investor, and the optimal wealth, as a function of state price density, drops faster for the CRRA investor than that for the loss averse investor.