Applications of Lévy Processes


Oleg Kudryavtsev (Editor) – Southern Federal University, Rostov-on-Don, Russia; Rostov Branch of the Russian Customs Academy, Rostov-on-Don, Russia
Antonino Zanette (Editor) – Department of Economics and Statistics, University of Udine, Udine, Italy

Series: Mathematics Research Developments

BISAC: MAT000000

Lévy processes have found applications in various fields, including physics, chemistry, long-term climate change, telephone communication, and finance. The most famous Lévy process in finance is the Black–Scholes model. This book presents important financial applications of Lévy processes. The Editors consider jump-diffusion and pure non-Gaussian Lévy processes, the multi-dimensional Black–Scholes model, and regime-switching Lévy models.

This book is comprised of seven chapters that focus on different approaches to solving applied problems under Lévy 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.




Chapter 1. Variance Reduction Applied to Machine Learning for Pricing Bermudan/American Options in High Dimension
(Ludovic Goudenège, Andrea Molent and Antonino Zanette – Fédération de Mathématiques de CentraleSupélec – CNRS, Gif-sur-Yvette, France, et al.)

Chapter 2. A Machine Learning Approach to Option Pricing under Lévy Processes
(Vasily Rodochenko and Oleg Kudryavtsev – Southern Federal University, Rostov-on-Don, Russia)

Chapter 3. On Swing Option Pricing Under Lévy Process Dynamics
(Justin Lars Kirkby and Shi-Jie Deng – School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, US)

Chapter 4. Fourier-Cosine Expansion Method for Pricing Equity-Indexed Annuities under Lévy Models
(Xiao Wei – China Institute for Actuarial Science, Central University of Finance and Economics, Beijing, China)

Chapter 5. The Multilevel Monte Carlo Method for Jump Lévy Models: Central Limit Theorem
(Mohamed Ben Alaya, Ahmed Kebaier and Thi Bao Tram Ngo – LMRS, CNRS (UMR 6085), Universit´e de Rouen Normandie, Saint Etienne du Rouvray, France, et al.)

Chapter 6. Optimal Resource Extraction in Regime Switching Lévy Markets
(Moustapha Pemy – Department of Mathematics, Towson University, Towson, Maryland, US)

Chapter 7. Numerical Methods for Pricing Options in Lévy Processes: The Approximate Wiener-Hopf Factorization Techniques
(Oleg Kudryavtsev and Alexander Grechko – Rostov branch of the Russian Customs Academy, Rostov-on-Don, Russia, et al.)


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