SOLVING THE IVANCEVIC OPTION PRICING MODEL
USING THE ELSAKI-ADOMIAN DECOMPOSITION METHOD
Oswaldo González-Gaxiola$^1$, J. Ruiz de Chávez$^2$
$^1$Departamento de Matemáticas Aplicadas y Sistemas
Universidad Autónoma Metropolitana-Cuajimalpa
Vasco de Quiroga 4871
Santa Fe, Cuajimalpa, 05348, MEXICO
$^{2}$ Departamento de Matemáticas
Universidad Autónoma Metropolitana-Iztapalapa
San Rafael Atlixco 186
Col. Vicentina, Iztapalapa, 09340, MEXICO
Abstract. In this paper, we propose a new computational algorithm called Elsaki-Adomian Decomposition Method (EADM) to solve a nonlinear Black-Scholes model recently established in [9], [10]. The proposed method is a combination of the Elsaki transform (ET) and the Adomian Decomposition Method (ADM). This new computational algorithm is applied directly without using any transformation, linearization, discretization or taking any additional restrictive assumption. Exact solutions of an illustrative example are successfully found by using the proposed method in order to show its reliability, efficiency, and accuracy.
AMS Subject Classification: 91G80, 35L05, 44A05
Key Words and Phrases: Ivancevic option pricing, Adomian decomposition method (ADM), Elsaki transform, Adomian polynomials


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DOI: 10.12732/ijam.v28i5.1

Volume: 28
Issue: 5
Year: 2015