0000000000291862
AUTHOR
Michel Fournié
Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation
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.
Global Linear Stability Analysis of the Flow Around a Superhydrophobic Circular Cylinder
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…
Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation
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.
High Order Compact Finite Difference Schemes for A Nonlinear Black-Scholes Equation
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.