Behavioral Portfolio Selection in Continuous Time

This paper formulates and studies a general continuous-time behavioural 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 It ˆo 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.