BEHAVIORAL PORTFOLIO SELECTION IN CONTINUOUS TIME

Mathematical Finance - Tập 18 Số 3 - Trang 385-426 - 2008
Hanqing Jin1, Xun Yu Zhou2
1The University of Oxford and National University of Singapore
2The University of Oxford and The Chinese University of Hong Kong

Tóm tắt

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 mis‐formulated (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.

Từ khóa


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Thông tin
Thông tin xuất bản

Mathematical Finance

Tập 18 Số 3

385-426

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