Derivation and solutions of some fractional Black-Scholes equations in coarse-grained space and time. Application to Merton's optimal portfolio

From MaRDI portal

Publication:980221

Jump to:navigation, search

DOI10.1016/j.camwa.2009.05.015zbMath1189.91230OpenAlexW1972754929MaRDI QIDQ980221

Guy Jumaric

Publication date: 28 June 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2009.05.015

zbMATH Keywords

fractional Brownian motion fractional stochastic differential equation fractional Taylor's series fractional Black-Scholes equation fractional merton's portfolio

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Fractional derivatives and integrals (26A33) Financial applications of other theories (91G80) Fractional partial differential equations (35R11)

Related Items

On a connection between a class of \(q\)-deformed algebras and the Hausdorff derivative in a medium with fractal metric, Option pricing beyond Black-Scholes based on double-fractional diffusion, Solving Black-Scholes equations using fractional generalized homotopy analysis method, A robust numerical scheme for a time-fractional Black-Scholes partial differential equation describing stock exchange dynamics, A closed-form approximation for the fractional Black-Scholes model with transaction costs, The analytical solution for the Black-Scholes equation with two assets in the Liouville-Caputo fractional derivative sense, Touchard wavelet technique for solving time-fractional Black-Scholes model, An adaptive moving mesh method for a time-fractional Black-Scholes equation, Application of two-dimensional Fibonacci wavelets in fractional partial differential equations arising in the financial market, Thermo-viscoelastic transversely isotropic rotating hollow cylinder based on three-phase lag thermoelastic model and fractional Kelvin-Voigt type, One-dimensional problem of a fractional order two-temperature generalized thermo-piezoelasticity, Fractional order two-temperature thermoelasticity with finite wave speed, A difference method with parallel nature for solving time-space fractional Black-Scholes model, The effect of magnetic field and initial stress on fractional order generalized thermoelastic half-space, Solution of time-space fractional Black-Scholes European option pricing problem through fractional reduced differential transform method, A robust numerical solution to a time-fractional Black-Scholes equation, Computational challenge of fractional differential equations and the potential solutions: a survey, Derivation of a new Merton's optimal problem presented by fractional stochastic stock price and its applications, Computational approach based on wavelets for financial mathematical model governed by distributed order fractional differential equation, Modified fractional thermoelasticity model with multi-relaxation times of higher order: application to spherical cavity exposed to a harmonic varying heat, On a two-dimensional fractional thermoelastic system with nonlocal constraints describing a fractional Kirchhoff plate, Theory of fractional order in electro-thermoelasticity, A space-time fractional derivative model for European option pricing with transaction costs in fractal market, On the numerical solution of time fractional Black-Scholes equation, Fractional order theory in thermoelastic solid with three-phase lag heat transfer, Calculations of fractional derivative option pricing models based on neural network, Computational algorithm for financial mathematical model based on European option, European option pricing models described by fractional operators with classical and generalized<scp>Mittag‐Leffler</scp>kernels, A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options, Design and analysis of a numerical method for fractional neutron diffusion equation with delayed neutrons, Fractional order heat conduction law in magneto-thermoelasticity involving two temperatures, Numerical analysis of nonlinear time‐fractional fluid models for simulating heat transport processes in porous medium, Electrified fractional nanofluid flow with suspended carbon nanotubes, Hahn hybrid functions for solving distributed order fractional Black–Scholes European option pricing problem arising in financial market, A high‐order and fast scheme with variable time steps for the time‐fractional Black‐Scholes equation, Parameter estimation for time-fractional Black-Scholes equation with S\&P 500 index option, Unnamed Item, Error and stability estimates of a time-fractional option pricing model under fully spatial-temporal graded meshes, Design and analysis of a high order computational technique for time‐fractional Black–Scholes model describing option pricing, Numerical solution of time-fractional Black-Scholes equation, The memory time effects for unsteady seas and oceans water flow through the limestone porous medium in the presence of chemical reaction and Soret effects, A New Compact Numerical Scheme for Solving Time Fractional Mobile-Immobile Advection-Dispersion Model, Numerical computations of fractional nonlinear Hartmann flow with revised heat flux model, A new operator splitting method for American options under fractional Black-Scholes models, Simulations of variable concentration aspects in a fractional nonlinear viscoelastic fluid flow, A class of intrinsic parallel difference methods for time-space fractional Black-Scholes equation, Unnamed Item, Theory of fractional order in generalized thermoelectric MHD, State-space approach for an infinite medium with a spherical cavity based upon two-temperature generalized thermoelasticity theory and fractional heat conduction, Plane waves in a fractional order micropolar magneto-thermoelastic half-space, Thermoelectric Viscoelastic Fluid with Fractional Integral and Derivative Heat Transfer, SPECTRALLY ACCURATE OPTION PRICING UNDER THE TIME-FRACTIONAL BLACK–SCHOLES MODEL, On the resilience of a fractional compartment model, Numerical approximation of a time-fractional Black-Scholes equation, Hygrothermoelastic response of a hollow cylinder based on a coupled time-fractional heat and moisture transfer model, Analytically pricing double barrier options based on a time-fractional Black-Scholes equation, Numerical solution of the time fractional Black-Scholes model governing European options, Finite difference/Fourier spectral for a time fractional Black-Scholes model with option pricing, Fast numerical simulation of a new time-space fractional option pricing model governing European call option, Solution of the fractional Black-Scholes option pricing model by finite difference method, Option pricing of a bi-fractional Black-Merton-Scholes model with the Hurst exponent \(H\) in \([\frac{1}{2}, 1\)], Stokes' first problem for a thermoelectric fluid with fractional-order heat transfer, A space-time spectral method for time-fractional Black-Scholes equation, On high-order schemes for tempered fractional partial differential equations, A compact finite difference scheme for fractional Black-Scholes option pricing model, A semianalytical solution of the fractional derivative model and its application in financial market, Thermo-viscoelastic materials with fractional relaxation operators, A universal difference method for time-space fractional Black-Scholes equation, Pricing of American carbon emission derivatives and numerical method under the mixed fractional Brownian motion, The numerical simulation of the tempered fractional Black-Scholes equation for European double barrier option, Efficient operator splitting and spectral methods for the time-space fractional Black-Scholes equation, Numerical method for a system of PIDEs arising in American contingent claims under FMLS model with jump diffusion and regime-switching process, Recovery of the time-dependent implied volatility of time fractional Black-Scholes equation using linearization technique, A high accuracy numerical method and its convergence for time-fractional Black-Scholes equation governing European options, A compact quadratic spline collocation method for the time-fractional Black-Scholes model, Transient thermoelastic response in a cracked strip of functionally graded materials via generalized fractional heat conduction, Approximation of time fractional Black-Scholes equation via radial kernels and transformations, A second order numerical method for the time-fractional Black-Scholes European option pricing model, Anomalous \(g\)-factors for charged leptons in a fractional coarse-grained approach, COMPACT FINITE DIFFERENCE SCHEMES OF THE TIME FRACTIONAL BLACK-SCHOLES MODEL, Fast solution method and simulation for the 2D time-space fractional Black-Scholes equation governing European two-asset option pricing, Optimal algebra and power series solution of fractional Black-Scholes pricing model, An efficient numerical scheme and its stability analysis for a time-fractional reaction diffusion model, The space-time coupled fractional Cattaneo-Friedrich Maxwell model with Caputo derivatives

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:980221&oldid=12970149"