Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment

Gordan Zitkovic

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arXiv · 0705.4487

Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment

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 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. 2007-05-30. Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment. https://arxiv.org/abs/0705.4487

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