With Applications in Finance
Focusing on optimal stopping and control, this advanced guide delves into Monte Carlo simulation and its financial applications. It caters to both quantitative finance practitioners and academic researchers, beginning with classical simulation-based algorithms before exploring innovative, cutting-edge methodologies currently in development.
Focusing on contemporary variance reduction methods, this book explores innovative approaches for Monte Carlo and Markov Chain Monte Carlo (MCMC) applications in machine learning and finance. It introduces new techniques such as martingale representations and Stein control variates alongside traditional methods. The text emphasizes the development and theoretical analysis of new variance reduction algorithms in MCMC, complemented by numerical examples that demonstrate the effectiveness of the proposed strategies.
The aim of this volume is to provide an extensive account of the most recent advances in statistics for discretely observed Lévy processes. These days, statistics for stochastic processes is a lively topic, driven by the needs of various fields of application, such as finance, the biosciences, and telecommunication. The three chapters of this volume are completely dedicated to the estimation of Lévy processes, and are written by experts in the field. The first chapter by Denis Belomestny and Markus Reiß treats the low frequency situation, and estimation methods are based on the empirical characteristic function. The second chapter by Fabienne Comte and Valery Genon-Catalon is dedicated to non-parametric estimation mainly covering the high-frequency data case. A distinctive feature of this part is the construction of adaptive estimators, based on deconvolution or projection or kernel methods. The last chapter by Hiroki Masuda considers the parametric situation. The chapters cover the main aspects of the estimation of discretely observed Lévy processes, when the observation scheme is regular, from an up-to-date viewpoint.