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Horizon-unbiased utility functions

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  • Henderson, Vicky
  • Hobson, David
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    Abstract

    In this paper we consider a class of mixed optimal control/optimal stopping problems related to the choice of the best time to sell a single unit of an indivisible asset. We assume that in addition to the indivisible asset, the agent has access to a financial market. Investments in the financial market can be used for hedging, but the financial assets are only partially correlated with the indivisible asset, so that the agent faces an incomplete markets problem. We show how, even in the infinite horizon case, it is possible to express the problem as a maximisation problem with respect to an inter-temporal utility function evaluated at the sale time, but that this objective function must satisfy consistency conditions over time.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 117 (2007)
    Issue (Month): 11 (November)
    Pages: 1621-1641

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    Handle: RePEc:eee:spapps:v:117:y:2007:i:11:p:1621-1641

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    Related research

    Keywords: Optimal stopping Stochastic control Utility maximisation Real options Incomplete market CRRA utility Horizon-unbiased utility Backward heat equation;

    References

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    1. McDonald, Robert & Siegel, Daniel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, MIT Press, vol. 101(4), pages 707-27, November.
    2. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373.
    3. A. Oberman & T. Zariphopoulou, 2003. "Pricing early exercise contracts in incomplete markets," Computational Management Science, Springer, vol. 1(1), pages 75-107, December.
    4. Hugonnier, Julien & Morellec, Erwan, 2007. "Corporate control and real investment in incomplete markets," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1781-1800, May.
    5. Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258.
    6. Tahir Choulli & Christophe Stricker, 2005. "Minimal Entropy-Hellinger Martingale Measure In Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 465-490.
    7. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
    8. Henderson, Vicky & Hobson, David G., 2002. "Real options with constant relative risk aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 27(2), pages 329-355, December.
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    Citations

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    Cited by:
    1. Henderson, Vicky, 2010. "Is corporate control effective when managers face investment timing decisions in incomplete markets?," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1062-1076, June.
    2. Timothy C. Johnson, 2013. "Reciprocity as the foundation of Financial Economics," Papers 1310.2798, arXiv.org.
    3. Christian-Oliver Ewald & Zhaojun Yang, 2008. "Utility based pricing and exercising of real options under geometric mean reversion and risk aversion toward idiosyncratic risk," Computational Statistics, Springer, vol. 68(1), pages 97-123, August.
    4. Tahir Choulli & Junfeng Ma, 2013. "Explicit Description of HARA Forward Utilities and Their Optimal Portfolios," Papers 1307.0785, arXiv.org.
    5. Grasselli, Matheus & Henderson, Vicky, 2009. "Risk aversion and block exercise of executive stock options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 109-127, January.
    6. Michail Anthropelos, 2011. "Forward Exponential Performances: Pricing and Optimal Risk Sharing," Papers 1109.3908, arXiv.org, revised Mar 2013.
    7. Sigrid Kallblad & Jan Obloj & Thaleia Zariphopoulou, 2013. "Time--consistent investment under model uncertainty: the robust forward criteria," Papers 1311.3529, arXiv.org.

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