  This paper studies a loss-averse version of the multiplicative habit
formation preference and the corresponding optimal investment and consumption
strategies over an infinite horizon. The agent's consumption preference is
depicted by a general S-shaped utility function of her consumption-to-habit
ratio. By considering the concave envelope of the S-shaped utility and the
associated dual value function, we provide a thorough analysis of the HJB
equation for the concavified problem via studying a related nonlinear free
boundary problem. Based on established properties of the solution to this free
boundary problem, we obtain the optimal consumption and investment policies in
feedback form. Some new and technical verification arguments are developed to
cope with generality of the utility function. The equivalence between the
original problem and the concavified problem readily follows from the structure
of the feedback policies. We also discuss some quantitative properties of the
optimal policies under several commonly used S-shaped utilities, complemented
by illustrative numerical examples and their financial implications.
