英文标题：
《A Framework for Analyzing Stochastic Jumps in Finance based on Belief
  and Knowledge》
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作者：
Takanori Adachi
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最新提交年份：
2016
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英文摘要：
  We introduce a formal language IE that is a variant of the language PAL developed in [van Benthem 2011] by adding a belief operator and a common belief operator,specializing to stochastic analysis. A constant symbol in the language denotes a stochastic process so that we can represent several financial events as formulae in the language, which is expected to be clues of analyzing the moments that some stochastic jumps such as financial crises occur based on knowledge and belief of individuals or those shared within groups of individuals. In order to represent beliefs, we use sigma-complete Boolean algebras as generalized sigma-algebras. We use the representation for constructing a model in which the interpretations of the formulae written in the language IE reside. The model also uses some new categories for integrating several components appeared in the theory into one.
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中文摘要：
我们介绍了一种形式语言IE，它是[van Benthem 2011]中开发的PAL语言的变体，通过添加一个信念算子和一个公共信念算子，专门用于随机分析。该语言中的常量符号表示一个随机过程，因此我们可以用该语言中的公式来表示多个金融事件，这有望成为分析某些随机跳跃（如金融危机）发生的时刻的线索，这些随机跳跃是基于个人的知识和信念或个人群体中共享的知识和信念。为了表示信念，我们使用sigma完全布尔代数作为广义sigma代数。我们使用这种表示法来构建一个模型，其中对用IE语言编写的公式进行了解释。该模型还使用了一些新的类别，将理论中出现的几个组成部分整合为一个。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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