Examples of Analytical Solutions by Means of Mittag-Leffler Function of Fractional Black-Scholes Option Pricing Equation

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Mohammad Hossein Akrami ◽  
Gholam Hussian Erjaee
Keyword(s):  
Option Pricing ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Financial Mathematics ◽  
Explicit Solutions ◽  
Analytical Technique ◽  
Variational Iteration ◽  
Black Scholes

AbstractIn this article, we have implemented reconstruction of variational iteration method as a new approximate analytical technique for solving fractional Black-Scholes option pricing equations. Indeed, we essentially use the well-known Mittag-Leffler function to obtain explicit solutions for some examples of financial mathematics equations.

scholarly journals Fractional Black-Scholes model with regularized Prabhakar derivative

2017 ◽  
Vol 102 (116) ◽  
pp. 121-132 ◽  
Author(s):  
Shiva Eshaghi ◽  
Alireza Ansari ◽  
Reza Ghaziani ◽  
Mohammadreza Darani
Keyword(s):  
Analytical Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
European Options ◽  
Variational Iteration ◽  
Black Scholes Model ◽  
Approximate Analytical Solutions ◽  
Black Scholes ◽  
Fractional Type

We introduce a fractional type Black-Scholes model in European options including the regularized Prabhakar derivative. We apply the reconstruction of variational iteration method to get the approximate analytical solutions for some models of generalized fractional Black-Scholes equations in terms of the generalized Mittag-Leffler functions.

scholarly journals APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

2020 ◽  
Vol 20 (3) ◽  
pp. 661-672
Author(s):  
JAWARIA TARIQ ◽  
JAMSHAD AHMAD
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Physical Phenomena ◽  
Convergent Solution

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

scholarly journals Analytical solutions of time-fractional advection problem

2016 ◽  
Vol 12 (6) ◽  
pp. 6286-6289
Author(s):  
Huimin Wang
Keyword(s):  
Analytical Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
The Other ◽  
Variational Iteration

we use variational iteration method (VIM) to solve some nonlinear time-fractional advection problem.Compared to the other method, the VIM is direct and straightforward.

scholarly journals Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing Model

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1642
Author(s):  
Ruyi Xing ◽  
Meng Liu ◽  
Kexin Meng ◽  
Shuli Mei
Keyword(s):  
Iteration Method ◽  
Exact Analytical Solution ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Haar Wavelet ◽  
Algebraic Equations ◽  
Haar Wavelet Transform ◽  
Variational Iteration ◽  
Black Scholes Model ◽  
Black Scholes

Compared with the linear Black–Scholes model, nonlinear models are constructed through taking account of more practical factors, such as transaction cost, and so it is difficult to find an exact analytical solution. Combining the Haar wavelet integration method, which can transform the partial differential equation into the system of algebraic equations, the homotopy perturbation method, which can linearize the nonlinear problems, and the variational iteration method, which can solve the large system of algebraic equations efficiently, a novel numerical method for the nonlinear Black–Scholes model is proposed in this paper. Compared with the traditional methods, it has higher efficiency and calculation precision.

scholarly journals Fractional Variational Iteration Method and Its Application to Fractional Partial Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kılıçman ◽  
Bachok M. Taib
Keyword(s):  
Iteration Method ◽  
Fractional Derivatives ◽  
Financial Models ◽  
Gordon Equation ◽  
Burgers Equation ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Liouville Derivative ◽  
Black Scholes ◽  
Klein Gordon

We use the fractional variational iteration method (FVIM) with modified Riemann-Liouville derivative to solve some equations in fluid mechanics and in financial models. The fractional derivatives are described in Riemann-Liouville sense. To show the efficiency of the considered method, some examples that include the fractional Klein-Gordon equation, fractional Burgers equation, and fractional Black-Scholes equation are investigated.

NEW COMPUTATIONAL APPROACHES FOR BIOPHYSICAL HEAT TRANSFER IN TISSUE UNDER ULTRASONIC WAVES: THE VARIATIONAL ITERATION AND CHEBYSCHEV SPECTRAL SIMULATIONS

2014 ◽  
Vol 14 (03) ◽  
pp. 1450043 ◽  
Author(s):  
ASSMA F. ELSAYED ◽  
O. ANWAR BÉG
Keyword(s):  
Heat Transfer ◽  
Iteration Method ◽  
Numerical Study ◽  
Variational Iteration Method ◽  
Ultrasonic Waves ◽  
Bioheat Transfer ◽  
Stability And Convergence ◽  
Analytical Technique ◽  
Variational Iteration ◽  
Non Linear

A mathematical and numerical study is presented for simulating temperature distribution in a two-dimensional tissue medium using Pennes bioheat transfer equation, when the tissue is subjected to ultrasonic waves. Following nondimensionalization of the governing partial differential equation, a novel variational iteration method (VIM) solution is developed. This excellent technique introduced by He [Variational iteration method — a kind of non-linear analytical technique: Some examples, Int J Non-Linear Mech.34:699–708, 1999] employs Lagrange multipliers which can be identified optimally via variational theory. The space and time distributions of temperature are studied and solutions visualized via Mathematica. The influence of thermal conductivity and relaxation time are also examined. Excellent stability and convergence characteristics of VIM are demonstrated. Validation is achieved with a Chebyschev spectral collocation method (CSCM). The present work demonstrates the excellent potential of this powerful semi-numerical method in nonlinear biological heat transfer and furthermore provides an alternative strategy to conventional finite element and finite difference computational simulations. The model finds applications in minimally-invasive spinal laser treatments, glaucoma therapy in ophthalmology and thermoradiotherapy for malignant tumors.

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