金融建模中的数值不变偏好
Numéraire-invariant preferences in financial modeling
摘要：
我们提供了一个公理化的基础上表示的数值不变的偏好的经济代理人在金融市场。在一个静态的环境中，简单的公理变成等价于下面的选择规则：代理人喜欢一个结果比另一个当且仅当预期（根据代理人的主观概率）相对于前者后者的相对回报率是非正的。随着传递性要求的增加，这最后一个偏好关系有一个扩展，可以用期望对数效用来表示。我们还处理的情况下，消费流的选择对象的动态环境。在那里，一个新的结果，关于规范表示的单位质量可选措施，使我们能够明确解决投资-消费问题，通过分离的两个方面的投资和消费。最后，我们给出了一个应用的最优数字投资问题与随机时间范围。
英文摘要：
We provide an axiomatic foundation for the representation of numéraire-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 numéraire investment with a random time-horizon.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
