This thesis consists of three applications of machine learning techniques to empirical asset pricing.
In the first part, which is co-authored work with Oksana Bashchenko, we develop a new method that detects jumps nonparametrically in financial time series ...
When a strict local martingale is projected onto a subfiltration to which it is not adapted, the local martingale property may be lost, and the finite variation part of the projection may have singular paths. This phenomenon has consequences for arbitrage ...
Given a two-dimensional smooth manifold M and a bijective pro jection p from M on a fixed plane (or a subset of that plane), we explore systematically how a wavelet transform (WT) on M may be generated from a plane WT by the inverse projection. Examples whe ...
A continuous interior penalty hp-finite element method that penalizes the jump of the discrete solution across mesh interfaces is introduced. Error estimates are obtained for first-order and advection-dominated transport operators. The analysis relies on t ...