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摘要翻译：
我们提供了一个公理基础来表示在金融市场中的经济主体的num{e}raire不变偏好。在静态环境中，简单的公理被证明等价于以下选择规则：代理人更喜欢一种结果而不是另一种结果，当且仅当后者相对于前者的预期（在代理人主观概率下）相对收益率是非正的。随着传递性要求的增加，最后一个偏好关系有了一个扩展，可以用期望的对数效用来表示。我们还讨论了消费流是选择对象的动态环境的情况。其中，关于单位质量可选测度的规范表示的一个新结果，使我们可以通过分离投资和消费两个方面来显式地解决投资-消费问题。最后，我们给出了具有随机时域的最优Num{e}raire投资问题的一个应用。
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英文标题：
《Num\'{e}raire-invariant preferences in financial modeling》
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作者：
Constantinos Kardaras
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最新提交年份：
2010
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
We provide an axiomatic foundation for the representation of num\'{e}raire-invariant preferences of economic agents acting in a financial market. In a static environment, the simple axioms turn out to be equivalent to the following choice rule: the agent prefers one outcome over another if and only if the expected (under the agent's subjective probability) relative rate of return of the latter outcome with respect to the former is nonpositive. With the addition of a transitivity requirement, this last preference relation has an extension that can be numerically represented by expected logarithmic utility. We also treat the case of a dynamic environment where consumption streams are the objects of choice. There, a novel result concerning a canonical representation of unit-mass optional measures enables us to explicitly solve the investment--consumption problem by separating the two aspects of investment and consumption. Finally, we give an application to the problem of optimal num\'{e}raire investment with a random time-horizon.
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PDF链接：
https://arxiv.org/pdf/0903.3736
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