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Optimal consumption and sale strategies for a risk averse agent

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  • David Hobson
  • Yeqi Zhu

Abstract

In this article we consider a special case of an optimal consumption/optimal portfolio problem first studied by Constantinides and Magill and by Davis and Norman, in which an agent with constant relative risk aversion seeks to maximise expected discounted utility of consumption over the infinite horizon, in a model comprising a risk-free asset and a risky asset with proportional transaction costs. The special case that we consider is that the cost of purchases of the risky asset is infinite, or equivalently the risky asset can only be sold and not bought. In this special setting new solution techniques are available, and we can make considerable progress towards an analytical solution. This means we are able to consider the comparative statics of the problem. There are some surprising conclusions, such as consumption rates are not monotone increasing in the return of the asset, nor are the certainty equivalent values of the risky positions monotone in the risk aversion.

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  • David Hobson & Yeqi Zhu, 2014. "Optimal consumption and sale strategies for a risk averse agent," Papers 1409.3394, arXiv.org.
    • Handle: RePEc:arx:papers:1409.3394
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    References listed on IDEAS

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    1. Ralf Korn, 1998. "Portfolio optimisation with strictly positive transaction costs and impulse control," Finance and Stochastics, Springer, vol. 2(2), pages 85-114.
    2. Vicky Henderson & David Hobson, 2013. "Risk Aversion, Indivisible Timing Options, and Gambling," Operations Research, INFORMS, vol. 61(1), pages 126-137, February.
    3. Svensson, Lars E. O. & Werner, Ingrid M., 1993. "Nontraded assets in incomplete markets : Pricing and portfolio choice," European Economic Review, Elsevier, vol. 37(5), pages 1149-1168, June.
    4. Vicky Henderson & David Hobson, 2008. "An explicit solution for an optimal stopping/optimal control problem which models an asset sale," Papers 0806.4061, arXiv.org, revised Nov 2008.
    5. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 7, pages 207-227, World Scientific Publishing Co. Pte. Ltd..
    6. 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.
    7. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    8. Duffie, Darrell & Sun, Tong-sheng, 1990. "Transactions costs and portfolio choice in a discrete-continuous-time setting," Journal of Economic Dynamics and Control, Elsevier, vol. 14(1), pages 35-51, February.
    9. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    10. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October.
    11. 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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    Cited by:

    1. David Hobson & Alex S. L. Tse & Yeqi Zhu, 2016. "Optimal consumption and investment under transaction costs," Papers 1612.00720, arXiv.org.

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