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Optimal stopping of constrained Brownian motion

Published online by Cambridge University Press:  14 July 2016

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

Keywords

OPTIMAL STOPPING OF MARKOV PROCESSESPROBABILISTIC POTENTIAL THEORYSUPERHARMONIC FUNCTIONSBALAYAGEDIFFUSION PROCESSESBROWNIAN MOTIONHEAT EQUATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 3 , June 1972 , pp. 557 - 571
Copyright
Copyright © Applied Probability Trust 1972 

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