All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 10 of 10

Showing per page

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...

First order second moment analysis for stochastic interface problems based on low-rank approximation

Helmut Harbrecht, Jingzhi Li (2013)

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

In this paper, we propose a numerical method to solve stochastic elliptic interface problems with random interfaces. Shape calculus is first employed to derive the shape-Taylor expansion in the framework of the asymptotic perturbation approach. Given the mean field and the two-point correlation function of the random interface, we can thus quantify the mean field and the variance of the random solution in terms of certain orders of the perturbation amplitude by solving a deterministic elliptic interface...

Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise

Georgios T. Kossioris, Georgios E. Zouraris (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider an initial and Dirichlet boundary value problem for a fourth-order linear stochastic parabolic equation, in one space dimension, forced by an additive space-time white noise. Discretizing the space-time white noise a modelling error is introduced and a regularized fourth-order linear stochastic parabolic problem is obtained. Fully-discrete approximations to the solution of the regularized problem are constructed by using, for discretization in space, a Galerkin finite element method...

Currently displaying 1 – 10 of 10

Page 1