Behavioral portfolio selection with loss control

Abstract

In this paper we formulate a continuous-time behavioral (à la cumulative prospect theory) portfolio selection model where the losses are constrained by a pre-specified upper bound. Economically the model is motivated by the previously proved fact that the losses occurring in a bad state of the world can be catastrophic for an unconstrained model. Mathematically solving the model boils down to solving a concave Choquet minimization problem with an additional upper bound. We derive the optimal solution explicitly for such a loss control model. The optimal terminal wealth profile is in general characterized by three pieces: the agent has gains in the good states of the world, gets a moderate, endogenously constant loss in the intermediate states, and suffers the maximal loss (which is the given bound for losses) in the bad states. Examples are given to illustrate the general results.

Dynamic consumption and portfolio choice under prospect theory

“…Define now Zhang, Jin, and Zhou (2011) show that if l t (x) is convex for every t ∈ [0, T ], then optimal dual consumption in the loss domain Q * c t,L Z Mt is given by −L t . Hence, optimal dual consumption c * t is given by…”

Greed, Leverage, and Potential Losses: A Prospect Theory Perspective

“…A CPT model with loss control can be formulated as follows: where a is a constant representing an exogenous cap on the losses allowed. This model is investigated in full in a companion paper Zhang, Jin, and Zhou (2011). It is shown that the optimal wealth profile, in its greatest generality, depends on three—instead of two—classes of states of the world, with an intermediate class of states between the good and the bad.…”

The optimal payoff for a Yaari investor

“…These alternative theories include the dual theory of Yaari (1987), the rank dependent utility (RDUT) approach of Quiggin (1993), and the cumulative prospect theory (CPT) of Tversky and Kahneman (1992). While optimal payoffs have been derived for an RDUT-investor (Carlier and Dana 2011, He and Zhou 2016, Xia and Zhou 2016, Xu 2016) and for a CPT investor (Jin and Zhou 2008, Zhang et al 2011, Rüschendorf and Vanduffel 2020, the optimal payoff for a Yaari investor is only known in some specific cases.…”