Utility maximization on the real line under proportional transaction costs

Bruno Bouchard ()
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Bruno Bouchard: Laboratoire de Probabilités et Modèles Aléatoires, University Pierre et Marie Curie, and LFA, CREST, 15 bd Gabriel Péri, 92245 Malakoff Cedex, France Manuscript

Finance and Stochastics, 2002, vol. 6, issue 4, 495-516

Abstract: 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.

Keywords: Transaction costs; utility maximization; reasonable asymptotic elasticity; hedging; option pricing (search for similar items in EconPapers)
JEL-codes: G11 G13 (search for similar items in EconPapers)
Date: 2002-08-19
Note: received: April 2001; final version received: November 2001
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Citations: View citations in EconPapers (29)

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