自生成和指数前向性能的双重刻画
A dual characterization of self-generation and exponential forward performances
摘要：
我们提出了一个数学框架，研究一个家庭的随机场-所谓的前瞻性表现-这是出现在金融数学的某些理性偏好关系的数值表示。它们的空间结构对应于效用函数，而时间结构反映了Nisio型半群的性质，称为自生成。在半鞅金融市场的背景下，我们在原有的自生成公式的基础上，给出了自生成公式的对偶形式，并证明了两者之间的等价性，从而给出了正向性能的对偶刻画.然后，我们专注于具有指数结构的随机场，并提供了必要和充分条件，在这种情况下的自我生成。最后，我们说明了我们的方法在金融市场驱动的伊藤过程，在那里我们得到了一个明确的参数化的所有指数向前性能。
英文摘要：
We propose a mathematical framework for the study of a family of random fields--called forward performances--which arise as numerical representation of certain rational preference relations in mathematical finance. Their spatial structure corresponds to that of utility functions, while the temporal one reflects a Nisio-type semigroup property, referred to as self-generation. In the setting of semimartingale financial markets, we provide a dual formulation of self-generation in addition to the original one, and show equivalence between the two, thus giving a dual characterization of forward performances. Then we focus on random fields with an exponential structure and provide necessary and sufficient conditions for self-generation in that case. Finally, we illustrate our methods in financial markets driven by Itô-processes, where we obtain an explicit parametrization of all exponential forward performances.
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