Behavioral Portfolio Selection with Loss Control

24 Pages Posted: 12 Feb 2010 Last revised: 17 Sep 2010

See all articles by Hanqing Jin

Hanqing Jin

Mathematical Institute; Oxford-Nie Financial Big Data Laboratory; St. Peter's College

Song Zhang

Peking University - School of Mathematical Science

Xun Yu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: February 8, 2010

Abstract

In this paper we formulate a continuous-time behavioral (a 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.

Keywords: Cumulative prospect theory, portfolio choice, gains and losses, constraint, Choquet integral, quantile function

JEL Classification: C62, E22, G11

Suggested Citation

Jin, Hanqing and Zhang, Song and Zhou, Xunyu, Behavioral Portfolio Selection with Loss Control (February 8, 2010). Available at SSRN: https://ssrn.com/abstract=1550715 or http://dx.doi.org/10.2139/ssrn.1550715

Hanqing Jin (Contact Author)

Mathematical Institute ( email )

Andrew Wiles Building
Radicliff Observatory Quarter, Woodstock Road
Oxford, oxfordshire OX2 6GG
United Kingdom

HOME PAGE: http://www.maths.ox.ac.uk

Oxford-Nie Financial Big Data Laboratory ( email )

Andrew Wiles Building
Woodstock Road
Oxford, Oxfordshire OX2 6GG
United Kingdom

St. Peter's College ( email )

New Inn Hall Street
Oxford, Oxfordshire OX1 2DL
United Kingdom

HOME PAGE: http://www.spc.ox.ac.uk

Song Zhang

Peking University - School of Mathematical Science ( email )

5 Yiheyuan Road
Beijing, 100871
China

Xunyu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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