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On the existence of shadow prices

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Date
2013
Link to item file
http://hal.archives-ouvertes.fr/hal-00645980/fr/
Dewey
Economie financière
Sujet
short selling constraints; shadow prices; Transaction costs
JEL code
D23
Journal issue
Finance and Stochastics
Volume
17
Number
4
Publication date
2013
Article pages
801-818
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00780-012-0201-4
URI
https://basepub.dauphine.fr/handle/123456789/7701
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Muhle-Karbe, Johannes
Kallsen, Jan
Campi, Luciano
Benedetti, Giuseppe
Type
Article accepté pour publication ou publié
Abstract (EN)
For utility maximization problems under proportional transaction costs, it has been observed that the original market with transaction costs can sometimes be replaced by a frictionless {\em shadow market} that yields the same optimal strategy and utility. However, the question of whether or not this indeed holds in generality has remained elusive so far. In this paper we present a counterexample which shows that shadow prices may fail to exist. On the other hand, we prove that short selling constraints are a sufficient condition to warrant their existence, even in very general multi-currency market models with possibly discontinuous bid-ask-spreads.

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