Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment
Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment
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随机时钟和无界随机禀赋的效用最大化
DOI：
10.1214/105051604000000738
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发表时间：
2005
影响因子：
1.8
通讯作者：
Gordan Zitkovic
中科院分区：
文献类型：
--
作者：
Gordan Zitkovic
我们引入有限加性测度的线性空间来处理随机时钟和无界随机禀赋过程下消费的最优预期效用问题。通过这种方式，我们建立了一大类效用最大化问题的存在性和唯一性，包括终端财富或消费的经典问题，以及依赖于随机时间范围或多个消费实例的问题。作为一个例子，我们明确地处理最大化消费流的对数效用的问题，其中 Ornstein-Uhlenbeck 过程的本地时间充当随机时钟。
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.