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Forward dynamic utility functions: A new model and new results

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  • Alghalith, Moawia
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    Abstract

    A major obstacle in the existing models of forward dynamic utilities and investment performance evaluation is to establish the existence and uniqueness of the optimal solutions. Consequently, we present a new model of forward dynamic utilities. In doing so, we establish the existence and uniqueness of the solutions for a general (smooth) utility function, and we show that the assumptions needed for such solutions are similar to those under the backward formulation. Moreover, we provide unique viscosity solutions. We also provide discontinuous viscosity solutions. In addition, we introduce Hausdorff-continuous viscosity solutions to the portfolio model.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712004985
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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 223 (2012)
    Issue (Month): 3 ()
    Pages: 842-845

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    Handle: RePEc:eee:ejores:v:223:y:2012:i:3:p:842-845

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Forward utility; Investment; Portfolio; Stochastic; Viscosity solutions; HJB PDE;

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    1. Tim Leung & Ronnie Sircar, 2009. "Accounting For Risk Aversion, Vesting, Job Termination Risk And Multiple Exercises In Valuation Of Employee Stock Options," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 99-128.
    2. Gordan \v{Z}itkovi\'c, 2008. "A dual characterization of self-generation and exponential forward performances," Papers 0809.0739, arXiv.org, revised Dec 2009.
    3. 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.
    4. Schroder, Mark & Skiadas, Costis, 2005. "Lifetime consumption-portfolio choice under trading constraints, recursive preferences, and nontradeable income," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 1-30, January.
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