Xunyu Zhou
Oxford and CUHK
Optimal Stopping under Probability Distortion
Abstract:
We formulate an optimal stopping problem where the probability scale is
distorted by a general nonlinear function. The problem is inherently
time inconsistent due to the Choquet integration involved. We
develop a new approach, based on a reformulation of the problem where one
optimally chooses the probability distribution or quantile function of the
stopped state. An optimal stopping time can then be recovered from the
obtained distribution/quantile function via the Skorokhod embedding. This
approach enables us to solve the problem in a fairly general manner with
different shapes of the payoff and probability distortion functions. In
particular, we show that the the exit time of an interval (corresponding
to the ``cutlossorstopgain" strategy widely adopted in stock trading)
is endogenously optimal for problems with convex distortion functions,
including ones where distortion is absent. We also discuss
economical interpretations of the results.
