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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 depending on a random time-horizon or multiple consumption instances. As an example we treat explicitly 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, 2007. "Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment," Papers 0705.4487, arXiv.org.
    • Handle: RePEc:arx:papers:0705.4487
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    File URL: http://arxiv.org/pdf/0705.4487
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