BEHAVIORAL PORTFOLIO SELECTION IN CONTINUOUS TIME
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
Tài liệu tham khảo
De Giorgi E., 2005, Second Order Stochastic Dominance, Reward‐Risk Portfolio Selection and CAPM, J. Finance Quant. Anal
Duffie D., 1996, Dynamic Asset Pricing Theory
Fishburn P. C., 1998, Nonlinear Preference and Utility Theory
He X., 2007, Behavioral Portfolio Choice: Model, Theory, and Equity Premium Puzzle, Working paper
Jin H., 2008, A Convex Stochastic Optimization Problem Arising from Portfolio Selection, Math. Finance, 81, 171, 10.1111/j.1467-9965.2007.00327.x
Karatzas I., 1998, Methods of Mathematical Finance
Von Neumann J., 1944, Theory of Games and Economic Behavior