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Computers and Mathematics with Applications, ISSN 0898-1221, 04/2018, Volume 75, Issue 8, pp. 2874 - 2887
In this paper a time-fractional Black–Scholes equation is examined. We transform the initial value problem into an equivalent integral–differential equation... 
Fractional differential equation | Singularity | Adapted mesh | Black–Scholes equation | Option valuation | AMERICAN | MATHEMATICS, APPLIED | FINITE-VOLUME METHOD | SPLINE COLLOCATION | ERROR ANALYSIS | Black-Scholes equation | DOUBLE-BARRIER OPTIONS | Analysis | Differential equations
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 04/2017, Volume 73, Issue 7, pp. 1566 - 1575
The purpose of this work is to apply the results developed by Chemin and David (2013, 2015), to the Black–Scholes equation. This latter equation being directly... 
Control | Black–Scholes equation | Shape parameters | Black-Scholes equation | MATHEMATICS, APPLIED | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics | Optimization and Control
Journal Article
Annals of Operations Research, ISSN 0254-5330, 10/2019, Volume 281, Issue 1, pp. 229 - 251
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 09/2018, Volume 62, pp. 164 - 173
In this paper, we investigate the non-linear Black–Scholes equation: and show that the one can be reduced to the equation by an appropriate point... 
Symmetry reduction | Black–Scholes equation | Exact solutions | LIE-ALGEBRAS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | Black-Scholes equation | OPTIONS | PHYSICS, MATHEMATICAL | Algebra | Quantitative Finance - Mathematical Finance
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 01/2020, Volume 363, pp. 464 - 484
This paper presents a high order numerical method based on a uniform mesh to obtain a highly accurate result for generalized Black–Scholes equation arising in... 
European call option | Stability analysis | Black–Scholes equation | Compact finite difference method | Convergence analysis | Crank–Nicolson method | SCHEME | MATHEMATICS, APPLIED | SPLINE COLLOCATION METHOD | Crank-Nicolson method | STABILITY | Black-Scholes equation | CONVERGENCE | Financial markets | Analysis | Methods | Differential equations
Journal Article
Computers & Mathematics with Applications, ISSN 0898-1221, 04/2017, Volume 73, Issue 7, p. 1566
The purpose of this work is to apply the results developed by Chemin and David (2013, 2015), to the Black-Scholes equation. This latter equation being directly... 
Studies | Black-Scholes equation | Stochastic models | Heat conductivity
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 10/2019, Volume 532
Merton has proposed a model for contingent claims on a firm as an option on the firms value, and is based on a generalization of the Black–Scholes stochastic... 
Option pricing models | Oscillator Hamiltonian | Merton's equation | Put–call parity | Beyond Black–Scholes | PHYSICS, MULTIDISCIPLINARY | Put-call parity | Beyond Black-Scholes
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2019, Volume 78, Issue 3, pp. 1037 - 1050
The aim of this paper is to explore the asymptotic properties of the solutions to the Black–Scholes equation. This paper focuses on the basic properties of... 
Volatility | Black–Scholes equation | Asymptotic behavior | Asymptotic properties | Formulas (mathematics)
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 07/2015, Volume 21, Issue 7, pp. 547 - 552
We construct the exact finite difference representation for a second-order, linear, Cauchy-Euler ordinary differential equation. This result is then used to... 
34A05 | sub-equations | 91G60 | 39A12 | 65N06 | Black-Scholes equation | exact finite difference schemes | 65L12 | Cauchy-Euler equation | Cauchy–Euler equation | Black–Scholes equation | MATHEMATICS, APPLIED
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 07/2014, Volume 19, Issue 7, pp. 2200 - 2211
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 06/2015, Volume 69, Issue 12, pp. 1407 - 1419
This paper investigates the pricing of double barrier options when the price change of the underlying is considered as a fractal transmission system. In this... 
Closed-form analytical solution | Fractional partial differential equation | Double barrier options | AMERICAN | MATHEMATICS, APPLIED | DIFFUSION | VALUATION | DRIVEN | Analysis | Pricing | Mathematical analysis | Barriers | Exact solutions | Black-Scholes equation | Mathematical models | Derivatives | Convergence
Journal Article
Social Studies of Science, ISSN 0306-3127, 12/2003, Volume 33, Issue 6, pp. 831 - 868
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 01/2018, Volume 41, Issue 2, pp. 697 - 704
This work presents a new model of the fractional Black‐Scholes equation by using the right fractional derivatives to model the terminal value problem. Through... 
fractional derivative | Black‐Scholes equation | asset pricing models | initial value problem | mathematical finance | terminal value problem | MATHEMATICS, APPLIED | PARTIAL-DIFFERENTIAL-EQUATIONS | Black-Scholes equation | EUROPEAN OPTIONS
Journal Article
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