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Factorization through Hilbert space and the dilation of L(X,Y)-valued measures

V. Mandrekar, P. Richard (1993)

Studia Mathematica

We present a general necessary and sufficient algebraic condition for the spectral dilation of a finitely additive L(X,Y)-valued measure of finite semivariation when X and Y are Banach spaces. Using our condition we derive the main results of Rosenberg, Makagon and Salehi, and Miamee without the assumption that X and/or Y are Hilbert spaces. In addition we relate the dilation problem to the problem of factoring a family of operators through a single Hilbert space.

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...

Feller semigroups and degenerate elliptic operators with Wentzell boundary conditions

Kazuaki Taira, Angelo Favini, Silvia Romanelli (2001)

Studia Mathematica

This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups with Wentzell boundary conditions in the characteristic case. Our results may be stated as follows: We can construct Feller semigroups corresponding to a diffusion phenomenon including absorption, reflection, viscosity, diffusion along the boundary and jump at each point of the boundary.

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