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

Author

Listed:
  • N. El Karoui

    (CMAP, LPMA)

  • Mohamed M'Rad

    (CMAP, LAGA)

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

  • N. El Karoui & Mohamed M'Rad, 2010. "Stochastic Utilities With a Given Optimal Portfolio : Approach by Stochastic Flows," Papers 1004.5192, arXiv.org, revised Apr 2013.
    • Handle: RePEc:arx:papers:1004.5192
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    References listed on IDEAS

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

    1. Levon Avanesyan & Mykhaylo Shkolnikov & Ronnie Sircar, 2020. "Construction of a class of forward performance processes in stochastic factor models, and an extension of Widder’s theorem," Finance and Stochastics, Springer, vol. 24(4), pages 981-1011, October.
    2. Sigrid Källblad & Jan Obłój & Thaleia Zariphopoulou, 2018. "Dynamically consistent investment under model uncertainty: the robust forward criteria," Finance and Stochastics, Springer, vol. 22(4), pages 879-918, October.
    3. Mahan Tahvildari, 2021. "Forward indifference valuation and hedging of basis risk under partial information," Papers 2101.00251, arXiv.org.

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