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.
@article{1107271667,
author = {\v Zitkovi\'c, Gordan},
title = {Utility maximization with a stochastic clock and an unbounded random endowment},
journal = {Ann. Appl. Probab.},
volume = {15},
number = {1A},
year = {2005},
pages = { 748-777},
language = {en},
url = {http://dml.mathdoc.fr/item/1107271667}
}
Žitković, Gordan. Utility maximization with a stochastic clock and an unbounded random endowment. Ann. Appl. Probab., Tome 15 (2005) no. 1A, pp. 748-777. http://gdmltest.u-ga.fr/item/1107271667/