Tensor numerical methods for multidimensional PDES: theoretical analysis and initial applications

Numerical Methods for PDEs

Numerical Methods for PDEs

Numerical Methods for Nonlinear PDEs in Finance

Many problems in finance can be posed in terms of an optimal stochastic control. Some well-known examples include transaction cost/uncertain volatility models [17, 2, 25], passport options [1, 26], unequal borrowing/lending costs in option pricing [9], risk control in reinsurance [23], optimal withdrawals in variable annuities[13], optimal execution of trades [20, 19], and asset allocation [28,...

Tensor-structured methods for parameter dependent and stochastic elliptic PDEs

Modern methods of tensor-product decomposition allow an efficient data-sparse approximation of functions and operators in higher dimensions [5]. The recent quantics-TT (QTT) tensor method allows to represent the multidimensional data with log-volume complexity [1, 2, 3]. We discuss the convergence rate of the Tucker, canonical and QTT stochastic collocation tensor approximations to the solution...

Adaptive Solution of Multidimensional PDEs via Tensor Product Wavelet Decomposition

In this paper we describe e cient adaptive discretization and solution of ellip tic PDEs which are forced by right hand side r h s with regions of smooth non oscillatory behavior and possibly localized regions with non smooth structures Clas sical discretization methods lead to dense representations for most operators The method described in this paper is based on the wavelet transformwhich pro...