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Optimal stopping of constrained Brownian motion

Published online by Cambridge University Press:  14 July 2016

Hans Föllmer*
Affiliation:
Dartmouth College, Hanover, New Hampshire

Abstract

We discuss the potential theory of optimal stopping for a standard process and an unbounded reward function. This is applied to Brownian motion constrained to a N(m, σ2) distribution at time 1. Boyce [2] has discovered, via computer, various interesting features of this example. We provide direct proofs for some of them, in particular for the qualitative jump of the optimal strategy as the variance σ2 passes the critical value 1.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1972 

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