Analytical Solutions of the Ivancevic Option Pricing Model With a Nonzero Adaptive Market Potential

Edeki, S.O.; Ugbebor, Olabisi O.; 'alez-Gaxiola, O. Gonz

doi:10.12732/ijpam.v115i1.14

Cited by 8 publications

(4 citation statements)

References 18 publications

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“…Figure 3 outlines the plot of the wave forms of the absolute, real, and imaginary parts of the complex bright soliton that is given by equation (72).Also for the same values k 1 � 1, ω 1 � 2, ω 2 � 2, equation ( 71) has a periodic solution. Based on equation ( 70), we write the solution as…”

Section: Physical Interpretationsmentioning

confidence: 99%

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Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

Elmandouh

Elbrolosy

2022

Journal of Mathematics

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The Ivancevic option pricing model comes as an alternative to the Black-Scholes model and depicts a controlled Brownian motion associated with the nonlinear Schrodinger equation. The applicability and practicality of this model have been studied by many researchers, but the analytical approach has been virtually absent from the literature. This study intends to examine some dynamic features of this model. By using the well-known ARS algorithm, it is demonstrated that this model is not integrable in the Painlevé sense. He’s variational method is utilized to create new abundant solutions, which contain the bright soliton, bright-like soliton, kinky-bright soliton, and periodic solution. The bifurcation theory is applied to investigate the phase portrait and to study some dynamical behavior of this model. Furthermore, we introduce a classification of the wave solutions into periodic, super periodic, kink, and solitary solutions according to the type of the phase plane orbits. Some 3D-graphical representations of some of the obtained solutions are displayed. The influence of the model’s parameters on the obtained wave solutions is discussed and clarified graphically.

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Section: Physical Interpretationsmentioning

confidence: 99%

“…e vector financial wave propagation were yanked in [71]. A nonzero adaptive market potential was analyzed in [72].…”

Section: Introductionmentioning

confidence: 99%

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

Elmandouh

Elbrolosy

2022

Journal of Mathematics

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“…In 2017, a model augmented by external atomic potentials was proposed to price European call options on a stock index [37]. In [38], a nonzero adaptive market potential was studied. Later, novel types of rogue wave and dark wave solutions were constructed for the Ivancevic option pricing model based on the trial function method [39].…”

Section: Introductionmentioning

confidence: 99%

Solitary Wave and Singular Wave Solutions for Ivancevic Option Pricing Model

Zeng

Liang

Yuan

2022

Mathematical Problems in Engineering

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The nonlinear option pricing model presented by Ivancevic is investigated. By using travelling wave transforming method, the nonlinear option pricing equation is transformed into a differential equation with constant coefficients. By solving the differential equation with F-expansion method, a series of exact solutions have been obtained for the Ivancevic option pricing model. By choosing appropriate parameter values, the dark-soliton and dark-soliton-like solutions, periodic wave solutions, and rogue wave solutions are obtained. These solutions will enrich the types of exact waves in the existing literature of the Ivancevic option pricing model. Furthermore, they may have potential uses in describing the possible physical mechanisms for wave phenomenon in financial markets.

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“…Considering the Harry-Dym equation being it nonlinear, most of the semianalytical methods such as Adomian Decomposition Method (ADM), Differential Transform Method (DTM), Homotopy Perturbation Method (HPM), etc., and their modified versions will require the involvement of Adomian polynomials but this is completely avoided via the NIM, yet high rate of accuracy and convergence is not neglected [5,6].…”

Section: Introductionmentioning

confidence: 99%

Iterative Method for Constructing Analytical Solutions to the Harry-Dym Initial Value Problem

'alez-Gaxiola¹,

'avez²,

Edeki³

2018

Int. J. of Appl. Math.

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In this paper, an analytical technique, namely the new iterative method (NIM), is applied to obtain an approximate analytical solution of the nonlinear Harry-Dym equation which is often used in the theory of solitons. The rapid convergence of the method results in qualitatively accurate solutions in relatively few iterations; this is obvious upon comparing the obtained analytical solutions with the exact solutions. Our results indicate that NIM is highly accurate and efficient, therefore can be considered a very useful and valuable method.

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Analytical Solutions of the Ivancevic Option Pricing Model With a Nonzero Adaptive Market Potential

Abstract: Cases of nonzero adaptive market potential are considered. The proposed method is proven to be direct, and effective as the obtained solutions tend rapidly to their exact forms.

Cited by 8 publications

References 18 publications

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

Solitary Wave and Singular Wave Solutions for Ivancevic Option Pricing Model

Iterative Method for Constructing Analytical Solutions to the Harry-Dym Initial Value Problem

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