David Hobson

Optimal Stopping, Prospect Theory and Naive Agents

Consider the problem of optimally stopping a time-homogeneous diffusion. In the classical setting the optimal strategy is a pure threshold strategy. But, if we consider prospect theory preferences then the optimal strategy is to aim for a target distribution which places mass on a continuum of points - the optimal stopping rule cannot be a pure threshold strategy. Moreover, the optimal prospect depends on the current value of the diffusion, and changes over time.

We solve the problem for the case of exponential Brownian motion and discuss one way to resolve the paradox of time-inconsistency.

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