Research articles
ScienceAsia (): 432-437 |doi:
10.2306/scienceasia1513-1874...432
Invariant subspace method for fractional Black-Scholes
equations
Pisamai Kittipoom
ABSTRACT: In this paper, the invariant subspace method is used to solve the time- and pricing-fractional Black-Scholes
equations, in which the fractional derivatives are described in the Caputo and Weyl sense, respectively. We introduce
invariant subspaces for time and pricing differential operators. Applying an appropriate invariant subspace will reduce
the fractional Black-Scholes equation to a system of ordinary fractional differential equations. Finally, using point
symmetries of the obtained system, we construct the explicit solutions of the fractional Black-Scholes equations.
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Applied Analysis Research Unit, Department of Mathematics, Faculty of Science,
Prince of Songkla University, Hat Yai, Songkhla 90112 Thailand |
* Corresponding author, E-mail: pisamai.k@psu.ac.th
Received 2 Mar 2018, Accepted 2 Dec 2018
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