## The Annals of Applied Probability

### Utility maximization with a stochastic clock and an unbounded random endowment

Gordan Žitković

#### 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.

#### Article information

Source
Ann. Appl. Probab., Volume 15, Number 1B (2005), 748-777.

Dates
First available in Project Euclid: 1 February 2005

https://projecteuclid.org/euclid.aoap/1107271667

Digital Object Identifier
doi:10.1214/105051604000000738

Mathematical Reviews number (MathSciNet)
MR2114989

Zentralblatt MATH identifier
1108.91032

Subjects
Primary: 91B28
Secondary: 60G99: None of the above, but in this section 60H99: None of the above, but in this section

#### Citation

Žitković, Gordan. Utility maximization with a stochastic clock and an unbounded random endowment. Ann. Appl. Probab. 15 (2005), no. 1B, 748--777. doi:10.1214/105051604000000738. https://projecteuclid.org/euclid.aoap/1107271667

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