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Maximizing functionals of the maximum in the Skorokhod embedding problem and an application to variance swaps

Abstract:

The Az\'{e}ma-Yor solution (resp., the Perkins solution) of the Skorokhod embedding problem has the property that it maximizes (resp., minimizes) the law of the maximum of the stopped process. We show that these constructions have a wider property in that they also maximize (and minimize) expected values for a more general class of bivariate functions $F(W_{\tau},S_{\tau})$ depending on the joint law of the stopped process and the maximum. Moreover, for monotonic functions $g$, they also maxi...

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Publisher copy:
10.1214/12-AAP893

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
Annals of Applied Probability
Volume:
23
Issue:
5
Pages:
2020-2052
Publication date:
2010-12-17
DOI:
ISSN:
1050-5164
URN:
uuid:cfd39734-c2af-4566-be74-844ec57dd368
Source identifiers:
369821
Local pid:
pubs:369821
Language:
English
Keywords:

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