期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 59, 期 3, 页码 1142-1164出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2009.05.015
关键词
Fractional stochastic differential equation; Fractional Brownian motion; Fractional Black-Scholes equation; Fractional Taylor's series; Fractional Merton's portfolio
By using the new fractional Taylor's series of fractional order f (x + h) = E-alpha (h(alpha)D(x)(alpha))f (x) where E-alpha (.) denotes the Mittag-Leffler function, and D-x(alpha) is the so-called modified Riemann-Liouville fractional derivative which we introduced recently to remove the effects of the non-zero initial value of the function under consideration, one can meaningfully consider a modeling of fractional stochastic differential equations as a fractional dynamics driven by a (usual) Gaussian white noise. One can then derive two new families of fractional Black-Scholes equations, and one shows how one can obtain their solutions. Merton's optimal portfolio is once more considered and some new results are contributed, with respect to the modeling on one hand, and to the solution on the other hand. Finally, one makes some proposals to introduce real data and virtual data in the basic equation of stock exchange dynamics. (C) 2009 Elsevier Ltd. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据