Browsing by Author "Ramoeletsi, Realeboha"

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    Application of lie symmetrics to solving fractional black-scholes option pricing model in financial mathematics
    (National University of Lesotho, 2022-10-21) Ramoeletsi, Realeboha; Kaibe, Bosiu, Ngaka Nchejane
    We perform Lie symmetry analysis to the fractional Black-Scholes option pricing model whose price evolution is described in terms of a partial di erential equation (PDE). As a result, new complete Lie symmetry group and in nitesimal generators of the one-dimensional fractional Black-Scholes pricing model are derived. Furthermore, we compute a family of exact invariant solutions that constitute the pricing models for the Black-Scholes model using the associated in nitesimal generators and the corresponding similarity reduction equations. Using known solutions, more solutions are generated via group point transformations