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Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment
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.Comment: Published at http://dx.doi.org/10.1214/105051604000000738 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
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