Ana-Maria Matache

Wavelet Galerkin pricing of American options on Levy driven assets

The price of an American-style contract on assets driven by a class of Markov processes containing, in particular, Lévy processes of pure jump type with infinite jump activity is expressed as the solution of a parabolic variational integro-differential inequality (PIDI). A Galerkin discretization in logarithmic price using a wavelet basis is presented. Log-linear complexity in each time-step is achieved by wavelet compression of the moment matrix of the price process’ jump measure and by wavelet preconditioning of the large matrix LCPs at each time-step. Efficiency is demonstrated by numerical experiments for pricing American put contracts on various jump-diffusion and pure jump models. Failure of the smooth pasting principle is observed for American put contracts for certain finite variation pure jump price processes.

Fast Numerical Solution of Parabolic Integrodifferential Equations with Applications in Finance

We numerically solve parabolic problems

Fourier mode analysis of layers in shallow shell deformations

u_t+\cA u=0

Sparse wavelet methods for option pricing under stochastic volatility

in

Homogenization via p -FEM for problems with microstructure

(0,T)\times\Omega

Generalized FEM for Homogenization Problems

,

Analysis of membrane locking in hp FEM for a cylindrical shell

T<\infty

Higher-order convex approximations of Young measures in optimal control

, where

Wavelet Filtering for Exact Controllability of the Wave Equation

\Omega\subset\mathbb{R}

Sparse Two-Scale FEM for Homogenization Problems

is a bounded interval and