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Mathematics 2018, 6(8), 129; https://doi.org/10.3390/math6080129

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

1
Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
2
Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
3
Centre of Excellence in Mathematics, Commission on Higher Education, Ministry of Education, 328 Sri Ayuthaya Road, Bangkok 10400, Thailand
4
School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, WA 6845, Australia
*
Author to whom correspondence should be addressed.
Received: 6 July 2018 / Revised: 18 July 2018 / Accepted: 20 July 2018 / Published: 25 July 2018
(This article belongs to the Special Issue Advances in Differential and Difference Equations with Applications)
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Abstract

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. View Full-Text
Keywords: Black-Scholes model; fractional derivatives; generalized Mittag-Leffer function; Laplace transform homotopy perturbation method Black-Scholes model; fractional derivatives; generalized Mittag-Leffer function; Laplace transform homotopy perturbation method
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Sawangtong, P.; Trachoo, K.; Sawangtong, W.; Wiwattanapataphee, B. The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense. Mathematics 2018, 6, 129.

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