金融事件导论

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摘要翻译：
在本文中，我们将证明，由作者本人（参见[2]、[3]和[4])引入并应用于金融问题的金融事件平面可以被认为是两种不同方式的纤维。第一个是自然的，当最后一个是自然的可微流形时，它表明自己与实线的切丛同构；第二种是在区间]-1，\rightarrow[内给定利率i的复利资本化状态引起的纤维化。此外，在本文中，我们在第一个纤维上定义了仿射连接，在这种情况下也是由给定利率i下的复利状态引起的。本文的最终目标是认识到，由复利地位决定的所有影响只不过是这样一个事实的后果，即金融事件的空间是一个具有特定仿射联系的纤维，因此它们是纯粹几何性质的后果，最后取决于由纤维上的联系决定的曲率。考虑了第二纤维的纤维集合的自然预序。作者在文[1]、[5]、[6]、[7]、[8]中对本文提出的理论在经济学和金融学中的适用性和可能的发展方向作了一些评论。
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英文标题：
《Fibrations of financial events》
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作者：
David Carf{\i}
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最新提交年份：
2011
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分类信息：

一级分类：Mathematics        数学
二级分类：Differential Geometry        微分几何
分类描述：Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
复形，接触，黎曼，伪黎曼和Finsler几何，相对论，规范理论，整体分析
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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
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英文摘要：
  In this paper we shall prove that the plane of financial events, introduced and applied to financial problems by the author himself (see [2], [3] and [4]) can be considered as a fibration in two different ways. The first one, the natural one, reveals itself to be isomorphic to the tangent- bundle of the real line, when the last one is considered as a differentiable manifold in the natural way; the second one is a fibration induced by the status of compound interest capitalization at a given rate i in the interval ] - 1, \rightarrow [. Moreover, in the paper we define on the first fibration an affine connection, also in this case induced by the status of compound interest at a given rate i. The final goal of this paper is the awareness that all the effects determined by the status of compound interest are nothing but the consequences of the fact that the space of financial events is a fibration endowed with a particular affine connection, so they are consequences of purely geometric properties, at last, depending upon the curvature determined by the connection upon the fibration. A natural preorder upon the set of fibers of the second fibration is considered. Some remarks about the applicability to economics and finance of the theories presented in the paper and about the possible developments are made in the directions followed in papers [1], [5], [6], [7], [8] of the author.
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PDF链接：
https://arxiv.org/pdf/1106.1774

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关键词：金融事件 last given 复利 联系 natural