The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense

Mathematics

Panumart Sawangtong¹  Kamonchat Trachoo²  Wannika Sawangtong²  Benchawan Wiwattanapataphee³ 

[1] Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand;Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand;School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, WA 6845, Australia;

关键词: Black-Scholes model;    fractional derivatives;    generalized Mittag-Leffer function;    Laplace transform homotopy perturbation method;   

DOI  :  10.3390/math6080129

来源: DOAJ

【 摘 要 】

It is well known that the Black-Scholes model is used to establish the behavior of the option pricing in the financial market. In this paper, we propose the modified version of Black-Scholes model with two assets based on the Liouville-Caputo fractional derivative. The analytical solution of the proposed model is investigated by the Laplace transform homotopy perturbation method.

【 授权许可】

Unknown