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Risk Aversion, Indivisible Timing Options, and Gambling

Author

Listed:
  • Vicky Henderson

    (Oxford-Man Institute, University of Oxford, Oxford OX2 6ED, United Kingdom)

  • David Hobson

    (Department of Statistics, University of Warwick, Coventry CV4 7AL, United Kingdom)

Abstract

In this paper we model the behavior of a risk-averse agent who seeks to maximize expected utility and who has an indivisible asset and a timing option over when to sell this asset. Our main contribution is to show that, contrary to intuition, optimal behavior for such a risk-averse agent can include risk-increasing gambles. For example, a manager with a choice over when to disinvest from a project, a private homeowner with a property to sell, or an employee with a grant of American-style stock options may be better off taking positions in other assets with zero Sharpe ratio that are uncorrelated with the underlying project, house, or stock price risk. The results have wider implications for the modeling and interpretation of portfolio optimization problems involving American-style timing decisions.

Suggested Citation

  • Vicky Henderson & David Hobson, 2013. "Risk Aversion, Indivisible Timing Options, and Gambling," Operations Research, INFORMS, vol. 61(1), pages 126-137, February.
  • Handle: RePEc:inm:oropre:v:61:y:2013:i:1:p:126-137
    DOI: 10.1287/opre.1120.1131
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    References listed on IDEAS

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    3. David Hobson & Yeqi Zhu, 2014. "Optimal consumption and sale strategies for a risk averse agent," Papers 1409.3394, arXiv.org.
    4. Vasquez, Markus, 2017. "Utility of wealth with many indivisibilities," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 20-27.
    5. Volker Krätschmer & Marcel Ladkau & Roger J. A. Laeven & John G. M. Schoenmakers & Mitja Stadje, 2018. "Optimal Stopping Under Uncertainty in Drift and Jump Intensity," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1177-1209, November.
    6. Choi, Kyoung Jin & Kwak, Minsuk & Shim, Gyoocheol, 2017. "Time preference and real investment," Journal of Economic Dynamics and Control, Elsevier, vol. 83(C), pages 18-33.
    7. Jakub Trybu{l}a, 2014. "Merton problem with one additional indivisible asset," Papers 1403.3223, arXiv.org.
    8. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    9. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.
    10. Tsionas, Mike G. & Mamatzakis, Emmanuel & Ongena, Steven, 2020. "Does risk aversion affect bank output loss? The case of the Eurozone," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1127-1145.

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