Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment
General Finance
2008-12-10 v1 Optimization and Control
Probability
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.
Cite
@article{arxiv.0705.4487,
title = {Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment},
author = {Gordan Zitkovic},
journal= {arXiv preprint arXiv:0705.4487},
year = {2008}
}