0000000000291862

AUTHOR

Michel Fournié

showing 4 related works from this author

Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation

2004

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.

Matrix difference equationFTCS schemeNumerical AnalysisPartial differential equationApplied MathematicsMathematical analysisCompact finite differenceNumerical solution of the convection–diffusion equationFinite difference coefficientCentral differencing schemeComputational MathematicsModeling and SimulationAnalysisCompact convergenceMathematicsESAIM: Mathematical Modelling and Numerical Analysis
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Global Linear Stability Analysis of the Flow Around a Superhydrophobic Circular Cylinder

2016

International audience; Over the last few years, superhydrophobic (SH) surfaces have been receiving an increasing attention in many scientific areas by virtue of their ability to enhance flow slip past solid walls and reduce the skin-friction drag. In the present study, a global linear-stability analysis is employed to investigate the influence of the SH-induced slip velocity on the primary instability of the 2D flow past a circular cylinder. The flow regions playing the role of 'wavemaker' are identified by considering the structural sensitivity of the unstable mode, thus highlighting the effect of slip on the global instability of the considered flow. In addition, a sensitivity analysis t…

Hopf BifurcationFlow (psychology)Direct numerical simulationSlip SurfaceSlip (materials science)01 natural sciencesInstability010305 fluids & plasmasPhysics and Astronomy (all)symbols.namesakeTheoretical physics0103 physical sciencesCylinder[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]010303 astronomy & astrophysicsHopf bifurcationPhysicsDirect Numerical SimulationStrouhal NumberMechanicsbody regionsDragsymbolsStrouhal numberSlip Length[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
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Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation

2004

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.

Nonlinear systemDiscretizationDifferential equationConvergence (routing)Finite differenceCompact finite differenceApplied mathematicsBlack–Scholes modelViscosity solutionHigh-order compact finite differences numerical convergence viscosity solution financial derivativesMathematics
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High Order Compact Finite Difference Schemes for A Nonlinear Black-Scholes Equation

2001

A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.

DiscretizationMathematical analysisFinite differenceFinite difference coefficientBlack–Scholes modelStability (probability)Parabolic partial differential equationNonlinear systemOption pricing transaction costs parabolic equations compact finite difference discretizationsValuation of optionsScheme (mathematics)Applied mathematicsddc:004General Economics Econometrics and FinanceFinanceMathematicsSSRN Electronic Journal
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