Fractional calculus and continuous-time finance

被引：640
|
作者：
Scalas, E
Gorenflo, R
Mainardi, F
机构：
[1] Univ Piemonte Orientale, Dipartimento Sci & Tecnol Avanzate, I-15100 Alessandria, Italy
[2] Ist Nazl Fis Nucl, Sez Torino, I-10125 Turin, Italy
[3] Free Univ Berlin, Erstes Matemat Inst, D-14195 Berlin, Germany
[4] Univ Bologna, Dipartimento Fis, I-40126 Bologna, Italy
[5] Ist Nazl Fis Nucl, Sez Bologna, I-40126 Bologna, Italy
来源：
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2000年 / 284卷 / 1-4期
关键词：
stochastic processes; random walk; statistical finance; econophysics;
D O I：
10.1016/S0378-4371(00)00255-7
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the Levy scaling form, follow as particular cases of the theory. The theory fully takes into account the non-Markovian and non-local character of financial time series. Predictions on the long-time behaviour of the waiting-time probability density are presented. Finally, a general scaling form is given, based on the solution of the fractional diffusion equation. (C) 2000 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：376 / 384
页数：9
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