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Utility Maximization on the Real Line under Proportional Transaction Costs

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Date
2002
Dewey
Probabilités et mathématiques appliquées
Sujet
option pricing; Transaction costs; utility maximization; reasonable asymptotic elasticity; hedging
JEL code
G11; G13
Journal issue
Finance and Stochastics
Volume
6
Number
4
Publication date
2002
Article pages
495-516
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s007800200068
URI
https://basepub.dauphine.fr/handle/123456789/1532
Collections
  • CEREMADE : Publications
Metadata
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Author
Bouchard, Bruno
Type
Article accepté pour publication ou publié
Abstract (EN)
We consider a financial market with costs as in Kabanov and Last (1999). Given a utility function defined on ${\mathbb R}$, we analyze the problem of maximizing the expected utility of the liquidation value of terminal wealth diminished by some random claim. We prove that, under the Reasonable asymptotic elasticity conditions introduced by Schachermayer (2000a), existence and duality hold in the class of targets that can be approximated by bounded from below strategies. Under some additional condition, we prove that the optimal target is indeed attainable. As an application, we obtain a dual formulation for the exponential reservation price.

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