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Multivariate utility maximization with proportional transaction costs and random endowment

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Author Info

  • Giuseppe Benedetti

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX, CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique)

  • Luciano Campi

    ()
    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX, FiME - Laboratoire de Finance des Marchés d'Energies - Université Paris Dauphine - Paris IX)

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    Abstract

    In this paper we deal with a utility maximization problem at finite horizon on a continuous-time market with conical (and time varying) constraints (particularly suited to model a currency market with proportional transaction costs). In particular, we extend the results in Campi and Owen (2011) to the situation where the agent is initially endowed with a random and possibly unbounded quantity of assets. We start by studying some basic properties of the value function (which is now defined on a space of random variables), then we dualize the problem following some convex analysis techniques which have proven very useful in this field of research. We finally prove the existence of a solution to the dual and (under an additional boundedness assumption on the endowment) to the primal problem. The last section of the paper is devoted to an application of our results to utility indifference pricing.

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    File URL: http://hal.archives-ouvertes.fr/docs/00/58/63/77/PDF/rand-endowment.pdf
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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00586377.

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    Date of creation: 15 Apr 2011
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    Handle: RePEc:hal:wpaper:hal-00586377

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00586377/en/
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    Web page: http://hal.archives-ouvertes.fr/

    Related research

    Keywords: Transaction costs ; Foreign exchange market ; Multivariate utility function ; Optimal portfolio ; Duality theory ; Random endowment ; Utility-based pricing;

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    References

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    1. Guasoni, Paolo & Lépinette-Denis, Emmanuel & Rásonyi, Miklós, 2012. "The fundamental theorem of asset pricing under transaction costs," Economics Papers from University Paris Dauphine 123456789/9300, Paris Dauphine University.
    2. Elyés Jouini & Moncef Meddeb & Nizar Touzi, 2004. "Vector-valued coherent risk measures," Finance and Stochastics, Springer, Springer, vol. 8(4), pages 531-552, November.
    3. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, Elsevier, vol. 66(1), pages 178-197, June.
    4. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, Springer, vol. 3(2), pages 237-248.
    5. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, Springer, vol. 5(2), pages 259-272.
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    Cited by:
    1. Christoph Czichowsky & Johannes Muhle-Karbe & Walter Schachermayer, 2012. "Transaction Costs, Shadow Prices, and Duality in Discrete Time," Papers 1205.4643, arXiv.org, revised Jan 2014.
    2. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the existence of shadow prices," Working Papers hal-00645980, HAL.
    3. Christoph Czichowsky & Walter Schachermayer, 2014. "Duality Theory for Portfolio Optimisation under Transaction Costs," Papers 1408.5989, arXiv.org.
    4. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the Existence of Shadow Prices," Papers 1111.6633, arXiv.org, revised Jan 2013.

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