IJPAM: Volume 108, No. 1 (2016)

STOCHASTIC BLACK-SCHOLES EQUATION WITH
TIME-FRACTIONAL DERIVATIVE ON THE HALF-LINE

J. Sanchez-Ortiz$^1$, M.P. Arciga-Alejandre$^2$,
F.J. Ariza-Hernandez$^3$, J.C. Hernandez-Pastrana$^4$
$^{1,2,3,4}$Faculty of Mathematics
University of Guerrero
Chilpancingo, 39087, Guerrero, MEXICO


Abstract. We investigate the pricing of options using a modified Black-Scholes equation with a time-fractional derivative and additive white noise on the half-line. We construct the Green function for the initial-boundary value problem adapting the main ideas of the Fokas method and we prove existence and uniqueness of solutions.

Received: March 8, 2016

AMS Subject Classification: 35C15, 35A22, 60G22

Key Words and Phrases: black-scholes, Fokas method, Caputo fractional derivative, Mittag-Leffler function

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DOI: 10.12732/ijpam.v108i1.14 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 1
Pages: 159 - 168


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