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Horizon-unbiased utility functions

  • Henderson, Vicky
  • Hobson, David
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    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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    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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    1. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258.
    4. 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.
    5. 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.
    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. 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.
    8. A. Oberman & T. Zariphopoulou, 2003. "Pricing early exercise contracts in incomplete markets," Computational Management Science, Springer, vol. 1(1), pages 75-107, December.
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