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Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment

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  • Gordan Zitkovic

Abstract

We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility-maximization problems including the classical ones of terminal wealth or consumption, as well as the problems that depend on a random time horizon or multiple consumption instances. As an example we explicitly treat the problem of maximizing the logarithmic utility of a consumption stream, where the local time of an Ornstein-Uhlenbeck process acts as a stochastic clock.

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  • Gordan Zitkovic, 2005. "Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment," Papers math/0503516, arXiv.org.
    • Handle: RePEc:arx:papers:math/0503516
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    File URL: http://arxiv.org/pdf/math/0503516
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    References listed on IDEAS

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    1. Julien Hugonnier & Dmitry Kramkov, 2004. "Optimal investment with random endowments in incomplete markets," Papers math/0405293, arXiv.org.
    2. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
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    Cited by:

    1. Constantinos Kardaras, 2009. "Num\'{e}raire-invariant preferences in financial modeling," Papers 0903.3736, arXiv.org, revised Nov 2010.
    2. Traian A Pirvu & Ulrich G Haussmann, 2007. "On Robust Utility Maximization," Papers math/0702727, arXiv.org.
    3. Keppo, Jussi & Meng, Xu & Sullivan, Michael G., 2007. "A computational scheme for the optimal strategy in an incomplete market," Journal of Economic Dynamics and Control, Elsevier, vol. 31(11), pages 3591-3613, November.
    4. Mark Owen & Gordan Zitkovic, 2007. "Optimal Investment with an Unbounded Random Endowment and Utility-Based Pricing," Papers 0706.0478, arXiv.org, revised Sep 2007.
    5. Xiang Yu, 2011. "Utility maximization with addictive consumption habit formation in incomplete semimartingale markets," Papers 1112.2940, arXiv.org, revised May 2015.
    6. Oleksii Mostovyi, 2011. "Optimal investment with intermediate consumption and random endowment," Papers 1110.2573, arXiv.org, revised Oct 2012.
    7. Kasper Larsen & Gordan v{Z}itkovi'c, 2011. "On utility maximization under convex portfolio constraints," Papers 1102.0346, arXiv.org, revised Feb 2013.
    8. Oleksii Mostovyi, 2011. "Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption," Papers 1107.5852, arXiv.org, revised Jul 2012.
    9. Xiang Yu, 2014. "Optimal Consumption under Habit Formation In Markets with Transaction Costs and Random Endowments," Papers 1408.1382, arXiv.org, revised Jul 2016.
    10. Robert Jarrow, 2018. "An Equilibrium Capital Asset Pricing Model in Markets with Price Jumps and Price Bubbles," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 1-33, June.
    11. Robert Jarrow, 2017. "A Capm With Trading Constraints And Price Bubbles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-39, December.

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