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Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment

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  • Gordan Zitkovic
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    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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    File URL: http://arxiv.org/pdf/math/0503516
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number math/0503516.

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    Date of creation: Mar 2005
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    Publication status: Published in Annals of Applied Probability 2005, Vol. 15, No. 1B, 748-777
    Handle: RePEc:arx:papers:math/0503516

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    Web page: http://arxiv.org/

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    1. (**), 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. Xiang Yu, 2011. "Utility Maximization with Addictive Consumption Habit Formation in Incomplete Semimartingale Markets," Papers 1112.2940, arXiv.org, revised Apr 2014.
    2. Constantinos Kardaras, 2009. "Num\'{e}raire-invariant preferences in financial modeling," Papers 0903.3736, arXiv.org, revised Nov 2010.
    3. Oleksii Mostovyi, 2011. "Optimal investment with intermediate consumption and random endowment," Papers 1110.2573, arXiv.org, revised Oct 2012.
    4. Traian A Pirvu & Ulrich G Haussmann, 2007. "On Robust Utility Maximization," Papers math/0702727, arXiv.org.
    5. Mark Owen & Gordan Zitkovic, 2007. "Optimal Investment with an Unbounded Random Endowment and Utility-Based Pricing," Papers 0706.0478, arXiv.org, revised Sep 2007.
    6. Oleksii Mostovyi, 2011. "Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption," Papers 1107.5852, arXiv.org, revised Jul 2012.
    7. 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.

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