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Optimal Brownian Stopping between radially symmetric marginals in general dimensions

Abstract:

Given an initial (resp., terminal) probability measure μ (resp., ν) on Rd, we characterize those optimal stopping times τ that maximize or minimize the functional E|B0−Bτ|α, α>0, where (Bt)t is Brownian motion with initial law B0∼μ and with final distribution --once stopped at τ-- equal to Bτ∼ν. The existence of such stopping times is guaranteed by Skorohod-type embeddings of probability measures in "subharmoic order" into Brownian motion. This problem is equivalent to an optimal mass tra...

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Publication status:
Not published
Peer review status:
Not peer reviewed
Version:
Author's original manuscript

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
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Publisher:
Cornell University Library Publisher's website
Journal:
arXiv Journal website
Publication date:
2017-11-08
Pubs id:
pubs:743839
URN:
uri:8950a7de-79af-43a0-bf83-19ba25b1f1d2
UUID:
uuid:8950a7de-79af-43a0-bf83-19ba25b1f1d2
Local pid:
pubs:743839

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