Exact solutions for time-fractional Fokker–Planck–Kolmogorov equation of Geometric Brownian motion via Lie point symmetries

Azadeh Naderifard (), Elham Dastranj and S. Reza Hejazi ()
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Azadeh Naderifard: Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran
Elham Dastranj: Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran
S. Reza Hejazi: Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran

International Journal of Financial Engineering (IJFE), 2018, vol. 05, issue 02, 1-15

Abstract: In this paper, the transition joint probability density function of the solution of geometric Brownian motion (GBM) equation is obtained via Lie group theory of differential equations (DEs). Lie symmetry analysis is applied to find new solutions for time-fractional Fokker–Planck–Kolmogorov equation of GBM. This analysis classifies the forms of the solutions for the equation by the similarity variables arising from the symmetry operators. Finally, an analytic method called invariant subspace method is applied in order to find another exact solution.

Keywords: Fokker–Planck equation; time-fractional PDE; geometric Brownian motion; lie symmetry (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S2424786318500093

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