Applications of generalized statistics in critical phenomena and financial markets

广义统计在关键现象和金融市场中的应用

• 批准号: 210762288
• 负责人: Professor Dr. Hagen Kleinert
• 金额: --
• 依托单位: Max-Planck-Institut für Wissenschaftsgeschichte (MPIWG)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/210762288?language=en
• 关键词: Applications; generalized; statistics; critical; phenomena

The aim of the present project is to apply methods and techniques known from nonequilibrium statistical physics and information theory to systems exhibiting generalized statistics. Broadly speaking, generalized statistics characterizes processes which have broad (or heavy-tail) distributions. The difficulty in working with generalized statistics lies in the fact that the Central Limit Theorem alongside with the usual methods of statistical physics cannot be applied. Theoretical qualification for such “non-canonical” distributions is provided by means of the generalized Central Limit Theorem of P. Lévy. Phenomena obeying generalized statistics are very diverse and structurally rich including fractional diffusion processes, multiparticle hadronic systems, multifractals, or volatility fluctuations. Primary focus of the project will be in presently intensely studied systems represented by distributions emerging either from the Rényi and Tsallis Maximum-Entropy prescription or from Superstatistics. Central applications will be in financial markets. The other goal is to develop Information Geometry for systems with a generalized statistics and apply it to theory of critical phenomena with a particular emphasize on defect-mediated phase transitions.

本项目的目的是将非平衡统计物理学和信息论中已知的方法和技术应用于表现出广义统计的系统。广义统计描述了具有宽（或重尾）分布的过程。广义统计学的困难在于中心极限定理和统计物理的常用方法不能一起应用。这种“非正则”分布的理论资格是由P. Lévy的广义中心极限定理提供的。服从广义统计的现象是非常多样的，结构丰富，包括分数扩散过程，多粒子强子系统，多重分形，或波动波动。该项目的主要重点将是目前正在深入研究的系统，这些系统由Rényi和Tsallis最大熵处方或超级统计学中出现的分布表示。主要应用将在金融市场。另一个目标是开发信息几何系统的广义统计，并将其应用于理论的临界现象，特别强调缺陷介导的相变。

项目成果

Green function of the double-fractional Fokker-Planck equation: path integral and stochastic differential equations.

双分数式福克-普朗克方程的格林函数：路径积分和随机微分方程

• DOI: 10.1103/physreve.88.052106
• 发表时间: 2013
• 期刊: Physical review. E, Statistical, nonlinear, and soft matter physics
• 作者: H. Kleinert;V. Zatloukal
• 通讯作者: V. Zatloukal

Classical field theories from Hamiltonian constraint: Canonical equations of motion and local Hamilton-Jacobi theory

来自哈密顿约束的经典场论：规范运动方程和局部哈密顿-雅可比理论

• DOI: 10.1142/s0219887816500729
• 发表时间: 2016
• 期刊: arXiv: Mathematical Physics
• 作者: V. Zatloukal

Local-time representation of path integrals.

路径积分的本地时间表示

• DOI: 10.1103/physreve.92.062137
• 发表时间: 2015
• 期刊: Physical review. E, Statistical, nonlinear, and soft matter physics
• 作者: P. Jizba;V. Zatloukal
• 通讯作者: V. Zatloukal

Option pricing beyond Black-Scholes based on double-fractional diffusion

• DOI: 10.1016/j.physa.2015.12.125
• 发表时间: 2016-05-01
• 期刊: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
• 影响因子: 3.3
• 作者: Kleinert, H.;Korbel, J.
• 通讯作者: Korbel, J.