Lie symmetry, exact solutions and conservation laws of time fractional Black–Scholes equation derived by the fractional Brownian motion

IF 0.6 Q4 MATHEMATICS, APPLIED

Journal of Applied Analysis Pub Date : 2024-01-11 DOI:10.1515/jaa-2023-0107

Jicheng Yu

引用次数: 0

Abstract

Abstract The Black–Scholes equation is an important analytical tool for option pricing in finance. This paper discusses the Lie symmetry analysis of the time fractional Black–Scholes equation derived by the fractional Brownian motion. Some exact solutions are obtained, the figures of which are presented to illustrate the characteristics with different values of the parameters. In addition, a new conservation theorem and a generalization of the Noether operators are developed to construct the conservation laws for the time fractional Black–Scholes equation.

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由分数布朗运动导出的时间分数布莱克-斯科尔斯方程的列对称性、精确解和守恒定律

摘要 Black-Scholes 方程是金融学中期权定价的重要分析工具。本文讨论了由分数布朗运动导出的时间分数 Black-Scholes 方程的李对称分析。本文得到了一些精确解，并用数字说明了不同参数值下的特征。此外，还提出了一个新的守恒定理和诺特算子的广义，以构建时间分数布莱克-斯科尔斯方程的守恒定律。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied Analysis MATHEMATICS, APPLIED-

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Journal of Applied Analysis is an international journal devoted to applications of mathematical analysis. Among them there are applications to economics (in particular finance and insurance), mathematical physics, mechanics and computer sciences. The journal also welcomes works showing connections between mathematical analysis and other domains of mathematics such as geometry, topology, logic and set theory. The journal is jointly produced by the Institute of Mathematics of the Technical University of Łódź and De Gruyter. Topics include: -applications of mathematical analysis (real and complex, harmonic, convex, variational)- differential equations- dynamical systems- optimization (linear, nonlinear, convex, nonsmooth, multicriterial)- optimal control- stochastic modeling and probability theory- numerical methods