Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs

Numerical methods for sparse recovery

These lecture notes are an introduction to methods recently developed for performing numerical optimizations with linear model constraints and additional sparsity conditions to solutions, i.e. we expect solutions which can be represented as sparse vectors with respect to a prescribed basis. Such a type of problems has been recently greatly popularized by the development of the field of nonadapt...

Numerical Methods for PDEs

Numerical Methods for PDEs

Numerical Solutions to PDEs with Financial Applications

We present details of the 1D PDE solver used in the OpenGamma Platform, showing how it can price European and American options, with and without barrier features. All the results in this paper we generated using MATLAB, and this code is included here www.opengamma.com/downloads/financial-pde-solving-matlab-examples.zip.

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,...