Geodesic
Application of Lie symmetries to solving modified Black-Scholes equation
Serdica Mathematical Journal, Tome 48 (2022) no. 4, pp. 219-234.

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We perform Lie symmetry analysis on the modified Black-Scholes model described as a partial differential equation (PDE). As a result, a new complete Lie symmetry group and infinitesimal generators of the one-dimensional modified fractional Black-Scholes model are derived. Furthermore, we compute a family of exact invariant solutions that constitute the modified fractional Black-Scholes model using the associated infinitesimal generators and the corresponding similarity reduction equations. Using known solutions, more solutions are generated via group point transformations.
Keywords: Lie point symmetries, modified Black-Scholes, financial mathematics, Lie algebra, invariant solution, 35-XX 
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Ramoeletsi, Realeboha; Kaibe, Bosiu; Nchejane, Ngaka. Application of Lie symmetries to solving modified Black-Scholes equation. Serdica Mathematical Journal, Tome 48 (2022) no. 4, pp. 219-234. http://geodesic.mathdoc.fr/item/SMJ2_2022_48_4_a1/