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Utility maximization on the real line under proportional transaction costs

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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)

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    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.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 6 (2002)
    Issue (Month): 4 ()
    Pages: 495-516

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    Handle: RePEc:spr:finsto:v:6:y:2002:i:4:p:495-516

    Note: received: April 2001; final version received: November 2001
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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: Transaction costs; utility maximization; reasonable asymptotic elasticity; hedging; option pricing;

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    Cited by:
    1. Westray, Nicholas & Zheng, Harry, 2009. "Constrained nonsmooth utility maximization without quadratic inf convolution," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1561-1579, May.
    2. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the existence of shadow prices," Working Papers hal-00645980, HAL.
    3. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the Existence of Shadow Prices," Papers 1111.6633, arXiv.org, revised Jan 2013.
    4. Nicholas Westray & Harry Zheng, 2011. "Minimal sufficient conditions for a primal optimizer in nonsmooth utility maximization," Finance and Stochastics, Springer, vol. 15(3), pages 501-512, September.
    5. Luciano Campi & Mark Owen, 2011. "Multivariate utility maximization with proportional transaction costs," Finance and Stochastics, Springer, vol. 15(3), pages 461-499, September.

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