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

Author

Listed:
  • Nicole El Karoui

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Mohamed M'Rad

    (LAGA - Laboratoire Analyse, Géométrie et Applications - UP8 - Université Paris 8 Vincennes-Saint-Denis - UP13 - Université Paris 13 - Institut Galilée - CNRS - Centre National de la Recherche Scientifique, CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Nicole El Karoui & Mohamed M'Rad, 2010. "Stochastic Utilities With a Given Optimal Portfolio : Approach by Stochastic Flows," Working Papers hal-00477380, HAL.
    • Handle: RePEc:hal:wpaper:hal-00477380
    Note: View the original document on HAL open archive server: https://hal.science/hal-00477380v2
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    References listed on IDEAS

    as
    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, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
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    Citations

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    Cited by:

    1. Sergey Nadtochiy & Thaleia Zariphopoulou, 2018. "Optimal contract for a fund manager, with capital injections and endogenous trading constraints," Papers 1802.09165, arXiv.org.
    2. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Papers 1404.1895, arXiv.org.
    3. Mahan Tahvildari, 2021. "Forward indifference valuation and hedging of basis risk under partial information," Papers 2101.00251, arXiv.org.
    4. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Papers 1404.1913, arXiv.org.
    5. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Working Papers hal-00974831, HAL.
    6. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Post-Print hal-00974831, HAL.
    7. Sergey Nadtochiy & Michael Tehranchi, 2013. "Optimal investment for all time horizons and Martin boundary of space-time diffusions," Papers 1308.2254, arXiv.org, revised Jan 2014.
    8. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad & El Karoui & Hillairet Caroline & Mrad Mohamed, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Working Papers hal-00974815, HAL.
    9. Nicole El Karoui & Mohamed Mrad, 2013. "An Exact Connection between two Solvable SDEs and a Nonlinear Utility Stochastic PDE," Post-Print hal-00477381, HAL.

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