摘要翻译：
我们提出了一个数学框架来研究一族随机场--称为前向性能--它是数学金融中某些合理偏好关系的数值表示。它们的空间结构对应于效用函数的空间结构，而时间结构反映了一种Nisio型半群性质，称为自生成。在半线性金融市场的背景下，我们在原有的自生成模型的基础上，给出了一个对偶的自生成模型，并证明了两者之间的等价性，从而给出了前向性能的对偶刻画。然后我们重点讨论了指数结构随机场，给出了在这种情况下自生成的充要条件。最后，我们在由IT过程驱动的金融市场中说明了我们的方法，其中我们得到了所有指数正向性能的显式参数化。
---
英文标题：
《A dual characterization of self-generation and exponential forward
  performances》
---
作者：
Gordan \v{Z}itkovi\'c
---
最新提交年份：
2009
---
分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
--
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
--
一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
--

---
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 It\^o-processes, where we obtain an explicit parametrization of all exponential forward performances.
---
PDF链接：
https://arxiv.org/pdf/0809.0739