摘要翻译:
我们将随机金融的经典理论嵌入到一个微分几何框架中,称为几何套利理论,并证明了将套利写成主纤维丛的曲率是可能的。--利用套利策略的完整性对套利策略进行参数化。--给出资产定价基本定理的微分同伦刻画。--用五项原则刻画几何套利理论,证明它们与经典随机金融理论是一致的。--对于封闭市场,在允许套利但最小化的情况下,导出市场投资组合和动态的均衡解。-->不允许套利。--证明了风险消失的无免费午餐条件蕴涵着零曲率条件。
---
英文标题:
《Geometric Arbitrage Theory and Market Dynamics Reloaded》
---
作者:
Simone Farinelli
---
最新提交年份:
2020
---
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: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
--
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:General Finance 一般财务
分类描述:Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
--
---
英文摘要:
We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to: --Write arbitrage as curvature of a principal fibre bundle. --Parameterize arbitrage strategies by its holonomy. --Give the Fundamental Theorem of Asset Pricing a differential homotopic characterization. --Characterize Geometric Arbitrage Theory by five principles and show they they are consistent with the classical theory of stochastic finance. --Derive for a closed market the equilibrium solution for market portfolio and dynamics in the cases where: -->Arbitrage is allowed but minimized. -->Arbitrage is not allowed. --Prove that the no-free-lunch-with-vanishing-risk condition implies the zero curvature condition.
---
PDF链接:
https://arxiv.org/pdf/0910.1671