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Optimal Timing For An Indivisible Asset Sale

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  • Jonathan Evans
  • Vicky Henderson
  • David Hobson

Abstract

In this paper, we investigate the pricing via utility indifference of the right to sell a non‐traded asset. Consider an agent with power utility who owns a single unit of an indivisible, non‐traded asset, and who wishes to choose the optimum time to sell this asset. Suppose that this right to sell forms just part of the wealth of the agent, and that other wealth may be invested in a complete frictionless market. We formulate the problem as a mixed stochastic control/optimal stopping problem, which we then solve. We determine the optimal behavior of the agent, including the optimal criteria for the timing of the sale. It turns out that the optimal strategy is to sell the non‐traded asset the first time that its value exceeds a certain proportion of the agent's trading wealth. Further, it is possible to characterize this proportion as the solution to a transcendental equation.

Suggested Citation

  • Jonathan Evans & Vicky Henderson & David Hobson, 2008. "Optimal Timing For An Indivisible Asset Sale," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 545-567, October.
    • Handle: RePEc:bla:mathfi:v:18:y:2008:i:4:p:545-567
    DOI: 10.1111/j.1467-9965.2008.00347.x
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    References listed on IDEAS

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    1. Wilmott,Paul & Howison,Sam & Dewynne,Jeff, 1995. "The Mathematics of Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521497893, October.
    2. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    3. Miao, Jianjun & Wang, Neng, 2007. "Investment, consumption, and hedging under incomplete markets," Journal of Financial Economics, Elsevier, vol. 86(3), pages 608-642, December.
    4. James E. Smith & Robert F. Nau, 1995. "Valuing Risky Projects: Option Pricing Theory and Decision Analysis," Management Science, INFORMS, vol. 41(5), pages 795-816, May.
    5. Hubalek, Friedrich & Schachermayer, Walter, 2004. "Optimizing expected utility of dividend payments for a Brownian risk process and a peculiar nonlinear ODE," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 193-225, April.
    6. Henderson, Vicky & Hobson, David, 2007. "Horizon-unbiased utility functions," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1621-1641, November.
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    Citations

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    Cited by:

    1. Tahir Choulli & Junfeng Ma, 2013. "Explicit Description of HARA Forward Utilities and Their Optimal Portfolios," Papers 1307.0785, arXiv.org.
    2. Tim Leung & Zheng Wang, 2016. "Optimal Risk-Averse Timing of an Asset Sale: Trending vs Mean-Reverting Price Dynamics," Papers 1610.08143, arXiv.org.
    3. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2019. "A multi-asset investment and consumption problem with transaction costs," Finance and Stochastics, Springer, vol. 23(3), pages 641-676, July.
    4. David Hobson & Yeqi Zhu, 2014. "Optimal consumption and sale strategies for a risk averse agent," Papers 1409.3394, arXiv.org.
    5. Alexander, Carol & Chen, Xi & Ward, Charles, 2021. "Risk-adjusted valuation for real option decisions," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 1046-1064.
    6. David Hobson & Yeqi Zhu, 2014. "Multi-asset consumption-investment problems with infinite transaction costs," Papers 1409.8037, arXiv.org.
    7. Carol Alexander & Xi Chen, 2021. "Model risk in real option valuation," Annals of Operations Research, Springer, vol. 299(1), pages 1025-1056, April.
    8. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2016. "A multi-asset investment and consumption problem with transaction costs," Papers 1612.01327, arXiv.org.
    9. Tim Leung & Zheng Wang, 2019. "Optimal risk-averse timing of an asset sale: trending versus mean-reverting price dynamics," Annals of Finance, Springer, vol. 15(1), pages 1-28, March.
    10. Jakub Trybu{l}a, 2014. "Merton problem with one additional indivisible asset," Papers 1403.3223, arXiv.org.
    11. Leippold, Markus & Stromberg, Jacob, 2017. "Strategic technology adoption and hedging under incomplete markets," Journal of Banking & Finance, Elsevier, vol. 81(C), pages 181-199.
    12. Vicky Henderson & David Hobson, 2013. "Risk Aversion, Indivisible Timing Options, and Gambling," Operations Research, INFORMS, vol. 61(1), pages 126-137, February.
    13. Erik Ekstrom & Juozas Vaicenavicius, 2015. "Optimal liquidation of an asset under drift uncertainty," Papers 1509.00686, arXiv.org.

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