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Utility Maximization on the Real Line under Proportional Transaction Costs

Bouchard, Bruno (2002), Utility Maximization on the Real Line under Proportional Transaction Costs, Finance and Stochastics, 6, 4, p. 495-516. http://dx.doi.org/10.1007/s007800200068

Type
Article accepté pour publication ou publié
Date
2002
Journal name
Finance and Stochastics
Volume
6
Number
4
Publisher
Springer
Pages
495-516
Publication identifier
http://dx.doi.org/10.1007/s007800200068
Metadata
Show full item record
Author(s)
Bouchard, Bruno
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.
Subjects / Keywords
option pricing; Transaction costs; utility maximization; reasonable asymptotic elasticity; hedging
JEL
G11 - Portfolio Choice; Investment Decisions
G13 - Contingent Pricing; Futures Pricing

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