Economy – Quantitative Finance – General Finance
Scientific paper
2007-05-30
Ann. Appl. Prob (2005), vol. 15, no. 1B, pp. 748-777
Economy
Quantitative Finance
General Finance
Scientific paper
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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