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Stochastic Utilities With a Given Optimal Portfolio : Approach by Stochastic Flows

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  • N. El Karoui

    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS : UMR7641, LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Pierre et Marie Curie (UPMC) - Paris VI - Université Paris VII - Paris Diderot)

  • Mohamed M'Rad

    ()
    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS : UMR7641, LAGA - Laboratoire Analyse, Géométrie et Applications - CNRS : UMR7539 - Université Paris XIII - Paris Nord - Université Paris VIII - Vincennes Saint-Denis - Institut Galilée)

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    Abstract

    The paper generalizes the construction by stochastic flows of consistent utility processes introduced by M. Mrad and N. El Karoui in (2010). The utilities random fields are defined from a general class of processes denoted by $\GX$. Making minimal assumptions and convex constraints on test-processes, we construct by composing two stochastic flows of homeomorphisms, all the consistent stochastic utilities whose the optimal-benchmark process is given, strictly increasing in its initial condition. Proofs are essentially based on stochastic change of variables techniques.

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    File URL: http://hal.archives-ouvertes.fr/docs/00/80/86/12/PDF/ArticleAbstraitAVRIL2013.pdf
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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00477380.

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    Date of creation: 01 Apr 2010
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    Handle: RePEc:hal:wpaper:hal-00477380

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00477380
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    Related research

    Keywords: Consistent utilities; progressive utilities; forward utility; performance criteria; horizon-unbiased utility; consistent utility; progressive utility; portfolio optimization; optimal portfolio; duality; minimal martingal measure; Stochastic flows of homeomorphisms;

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    1. Tahir Choulli & Christophe Stricker & Jia Li, 2007. "Minimal Hellinger martingale measures of order q," Finance and Stochastics, Springer, vol. 11(3), pages 399-427, July.
    2. Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney.
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