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Behavioral portfolio selection in continuous time (2008)
| Venue: | Mathematical Finance |
| Citations: | 20 - 2 self |
BibTeX
@ARTICLE{Jin08behavioralportfolio,
author = {Hanqing Jin and Xun Yu Zhou},
title = {Behavioral portfolio selection in continuous time},
journal = {Mathematical Finance},
year = {2008}
}
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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.
Keyphrases
continuous time behavioral portfolio selection prospect theory bad one asset price certain class complete market two-piece crra utility s-shaped utility optimal terminal wealth position ill-posed model different component utility model behavioral model well-posed model behavioral criterion probability distortion gambling policy simple structure reminiscent systematic approach good state conventional expected utility maximization model admissible parameter risky allocation general result explicit form
