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Utility maximization on the real line under proportional transaction costs

Author

Listed:
  • 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)

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.

Suggested Citation

  • Bruno Bouchard, 2002. "Utility maximization on the real line under proportional transaction costs," Finance and Stochastics, Springer, vol. 6(4), pages 495-516.
    • 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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    More about this item

    Keywords

    Transaction costs; utility maximization; reasonable asymptotic elasticity; hedging; option pricing;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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