BEHAVIORAL PORTFOLIO SELECTION IN CONTINUOUS TIME

By Hanqing Jin, Xun Yu Zhou. 2007

325 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/f356264f287106f3be5639ab2ec69302bfd321eb

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Citations in the corpus

ON OPTIMAL INVESTMENT FOR A BEHAVIORAL INVESTOR IN MULTIPERIOD INCOMPLETE MARKET MODELS (2015, unknown): “The reason for this, as pointed out in Jin and Zhou [2008], is the presence of massively diﬃcult obstacles: the objective function is non-concave and the probability distortions make it impossible to use dynamic programming and the related machinery based on the Bellmann equation.”
Thou shalt buy and hold (2008, background): “The continuous-time Markowitz model (Richardson 1989, Zhou and Li 2000) or the recent behavioural portfolio selection model (Jin and Zhou 2008) both lead to similar continuously rebalancing optimal portfolios, even in the Black– Scholes case where there is only one stock available.”
OPTIMAL INSURANCE DESIGN UNDER RANK‐DEPENDENT EXPECTED UTILITY (2015, unknown): “An alternative definition is Vrdeu (W) = ∫ ∞0 T(P {U(W) t})dt, as used by Bernard and Ghossoub (2010) and Jin and Zhou (2008).”
Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment (2011, background): “In the 1970s Kahneman and Tversky (1979) proposed prospect theory (PT) for decision making under uncertainty.”
Static portfolio choice under Cumulative Prospect Theory (2010, background): “ Jin and Zhou (2008) use a similar form to (6).”
OPTIMAL DEMAND FOR CONTINGENT CLAIMS WHEN AGENTS HAVE LAW INVARIANT UTILITIES (2010, background): “KEY WORDS: demand, law invariant utilities, quantiles, constrained optimization.”
ARROW–DEBREU EQUILIBRIA FOR RANK‐DEPENDENT UTILITIES (2016, unknown): “Jin and Zhou (2008) and He and Zhou (2011a, 2016) developed a method called “quantile formulation” to overcome this technical obstacle.5 This formulation leads to a concave maximization problem when the quantile function of the future consumption is chosen as the decision variable.”