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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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    File URL: http://arxiv.org/pdf/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.
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