A semianalytical solution of the fractional derivative model and its application in financial market

DOI10.1155/2018/1872409zbMath1398.91615OpenAlexW2795163921WikidataQ130016740 ScholiaQ130016740MaRDI QIDQ1791055

Lina Song

Publication date: 4 October 2018

Published in: Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2018/1872409

zbMATH Keywords

fractional differential equationfinancial theoryAdomian decomposition method with the finite difference methodEuropean option pricing model

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Financial applications of other theories (91G80) Derivative securities (option pricing, hedging, etc.) (91G20) Fractional partial differential equations (35R11)

Related Items (2)

Numerical study on fractional-order Lotka-Volterra model with spectral method and Adams-Bashforth-Moulton method ⋮ An analytical approach for the fractional-order Hepatitis B model using new operator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Pricing of Options and Corporate Liabilities
• A new improved Adomian decomposition method and its application to fractional differential equations
• A second order explicit finite difference method for the fractional advection diffusion equation
• Notes on the homotopy analysis method: some definitions and theorems
• An optimal homotopy-analysis approach for strongly nonlinear differential equations
• Stock exchange fractional dynamics defined as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black-Scholes equations
• Option pricing of a bi-fractional Black-Merton-Scholes model with the Hurst exponent \(H\) in \([\frac{1}{2}, 1\)]
• Derivation and solutions of some fractional Black-Scholes equations in coarse-grained space and time. Application to Merton's optimal portfolio
• A comparison of numerical solutions of fractional diffusion models in finance
• A review of the decomposition method in applied mathematics
• Solving frontier problems of physics: the decomposition method
• A space-time fractional derivative model for European option pricing with transaction costs in fractal market
• Fractional integral associated to the self-similar set or the generalized self-similar set and its physical interpretation
• Analytically pricing double barrier options based on a time-fractional Black-Scholes equation
• A novel implicit finite difference method for the one-dimensional fractional percolation equation
• Analytically pricing European-style options under the modified Black-Scholes equation with a spatial-fractional derivative
• Fractional diffusion equation on fractals: one-dimensional case and asymptotic behaviour
• Analysis of the compact difference scheme for the semilinear fractional partial differential equation with time delay

This page was built for publication: A semianalytical solution of the fractional derivative model and its application in financial market