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.
Citation
Gordan Žitković. "Utility maximization with a stochastic clock and an unbounded random endowment." Ann. Appl. Probab. 15 (1B) 748 - 777, February 2005. https://doi.org/10.1214/105051604000000738
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