Applications of Levy Processes

ISBN-13: 9781536195255

Oleg Kudryavtsev

Opis

Levy processes have found applications in various fields, including physics, chemistry, long-term climate change, telephone communication, and finance. The most famous Levy process in finance is the BlackaScholes model. This book presents important financial applications of Levy processes. The Editors consider jump-diffusion and pure non-Gaussian Levy processes, the multi-dimensional BlackaScholes model, and regime-switching Levy models. This book is comprised of seven chapters that focus on different approaches to solving applied problems under Levy processes: Monte Carlo simulations, machine learning, the frame projection method, dynamic programming, the Fourier cosine series expansion, finite difference schemes, and the Wiener-Hopf factorization. Various numerical examples are carefully presented in tables and figures to illustrate the methods designed in the book.