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APPROXIMATE SOLUTION OF FRACTIONAL BLACK-SCHOLE’S EUROPEAN OPTION PRICING EQUATION BY USING ETHPM
Pradip R. Bhadane,KIRTIWANT P. GHADLE,AHMED A. HAMOUD 경남대학교 기초과학연구소 2020 Nonlinear Functional Analysis and Applications Vol.25 No.2
We proposed a new reliable combination of new Homotopy Perturbation Method(HPM) and Elzaki transform called as Elzaki Transform Homotopy Perturbation Method(ETHPM) is designed to obtain a exact solution to the fractional Black-Scholes equationwith boundary condition for a European option pricing problem. The fractional derivativeis in Caputo sense and the nonlinear terms in Fractional Black-Scholes Equation can behandled by using HPM. The Black-Scholes formula is used as a model for valuing Europeanor American call and put options on a non-dividend paying stock. The methods give ananalytic solution of the fractional Black-Scholes equation in the form of a convergent series. Finally, some examples are included to demonstrate the validity and applicability of theproposed technique.