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Fast convergence of the Coiflet-Galerkin method for general elliptic BVPs

Hani Akbari (2013)

International Journal of Applied Mathematics and Computer Science

We consider a general elliptic Robin boundary value problem. Using orthogonal Coifman wavelets (Coiflets) as basis functions in the Galerkin method, we prove that the rate of convergence of an approximate solution to the exact one is O(2−nN ) in the H 1 norm, where n is the level of approximation and N is the Coiflet degree. The Galerkin method needs to evaluate a lot of complicated integrals. We present a structured approach for fast and effective evaluation of these integrals via trivariate connection...

Fast deterministic pricing of options on Lévy driven assets

Ana-Maria Matache, Tobias Von Petersdorff, Christoph Schwab (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Arbitrage-free prices u of European contracts on risky assets whose log-returns are modelled by Lévy processes satisfy a parabolic partial integro-differential equation (PIDE) t u + 𝒜 [ u ] = 0 . This PIDE is localized to bounded domains and the error due to this localization is estimated. The localized PIDE is discretized by the θ -scheme in time and a wavelet Galerkin method with N degrees of freedom in log-price space. The dense matrix for 𝒜 can be replaced by a sparse matrix in the wavelet basis, and the linear...

Fast deterministic pricing of options on Lévy driven assets

Ana-Maria Matache, Tobias von Petersdorff, Christoph Schwab (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Arbitrage-free prices u of European contracts on risky assets whose log-returns are modelled by Lévy processes satisfy a parabolic partial integro-differential equation (PIDE) t u + 𝒜 [ u ] = 0 . This PIDE is localized to bounded domains and the error due to this localization is estimated. The localized PIDE is discretized by the θ-scheme in time and a wavelet Galerkin method with N degrees of freedom in log-price space. The dense matrix for 𝒜 can be replaced by a sparse matrix in the wavelet basis, and the...

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