Fluctuations of Lévy Processes with Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fluctuations of Lévy Processes with Applications write by Andreas E. Kyprianou. This book was released on 2014-01-09. Fluctuations of Lévy Processes with Applications available in PDF, EPUB and Kindle. Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.
Introductory Lectures on Fluctuations of Lévy Processes with Applications
Introductory Lectures on Fluctuations of Lévy Processes with Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introductory Lectures on Fluctuations of Lévy Processes with Applications write by Andreas E. Kyprianou. This book was released on 2006-12-18. Introductory Lectures on Fluctuations of Lévy Processes with Applications available in PDF, EPUB and Kindle. This textbook forms the basis of a graduate course on the theory and applications of Lévy processes, from the perspective of their path fluctuations. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical transparency and explicitness.
Fluctuations of Levy Processes with Applications
Fluctuations of Levy Processes with Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fluctuations of Levy Processes with Applications write by Andreas E. Kyprianou. This book was released on 2014-01-31. Fluctuations of Levy Processes with Applications available in PDF, EPUB and Kindle.
Financial Modelling with Jump Processes
Financial Modelling with Jump Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Financial Modelling with Jump Processes write by Peter Tankov. This book was released on 2003-12-30. Financial Modelling with Jump Processes available in PDF, EPUB and Kindle. WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic
Applications of Lévy Processes
Applications of Lévy Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Applications of Lévy Processes write by Oleg Kudryavtsev. This book was released on 2021. Applications of Lévy Processes available in PDF, EPUB and Kindle. "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"--
