Behavioral Portfolio Selection in Continuous Time

42 Pages Posted: 16 Jun 2008

See all articles by Hanqing Jin

Hanqing Jin

National University of Singapore (NUS)

Xun Yu Zhou

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management

Abstract

This paper formulates and studies a general continuous-time behavioral portfolio selection model under Kahneman and Tversky's (cumulative) prospect theory, featuring S-shaped utility (value) functions and probability distortions. Unlike the conventional expected utility maximization model, such a behavioral model could be easily misformulated (a.k.a. ill-posed) if its different components do not coordinate well with each other. Certain classes of an ill-posed model are identified. A systematic approach, which is fundamentally different from the ones employed for the utility model, is developed to solve a well-posed model, assuming a complete market and general Itô processes for asset prices. The optimal terminal wealth positions, derived in fairly explicit forms, possess surprisingly simple structure reminiscent of a gambling policy betting on a good state of the world while accepting a fixed, known loss in case of a bad one. An example with a two-piece CRRA utility is presented to illustrate the general results obtained, and is solved completely for all admissible parameters. The effect of the behavioral criterion on the risky allocations is finally discussed.

Suggested Citation

Jin, Hanqing and Zhou, Xun Yu, Behavioral Portfolio Selection in Continuous Time. Mathematical Finance, Vol. 18, No. 3, pp. 385-426, July 2008, Available at SSRN: https://ssrn.com/abstract=1144912 or http://dx.doi.org/10.1111/j.1467-9965.2008.00339.x

Hanqing Jin

National University of Singapore (NUS) ( email )

1E Kent Ridge Road
NUHS Tower Block Level 7
Singapore, 119228
Singapore

Xun Yu Zhou (Contact Author)

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management ( email )

Shatin, New Territories
Hong Kong
852 2609-8320 (Phone)
852 2603-5505 (Fax)

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