Efficient Evaluation Of Expectations Of Functions Of A Stable Levy Process And Its Extremum PDF Download
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Author | : Svetlana Boyarchenko |
Publisher | : |
Total Pages | : 0 |
Release | : 2022 |
Genre | : |
ISBN | : |
Download Efficient Evaluation of Expectations of Functions of a Stable Levy Process and Its Extremum Book in PDF, ePub and Kindle
Integral representations for expectations of functions of a stable L 'evy process $X$ and its supremum $ bar X$ are derived. As examples, cumulative probability distribution functions (cpdf) of $X_T, barX_T$, the joint cpdf of $X_T$ and $ barX_T$, and the expectation of $( be X_T- barX_T)_+$, $ be>1$, are considered, and efficient numerical procedures for cpdfs are developed. The most efficient numerical methods use the conformal acceleration technique and simplified trapezoid rule.
Author | : Svetlana Boyarchenko |
Publisher | : |
Total Pages | : 0 |
Release | : 2022 |
Genre | : |
ISBN | : |
Download Efficient Evaluation of Expectations of Functions of a Lévy Process and Its Extremum. II. Book in PDF, ePub and Kindle
We prove a simple general formula for the expectation of a function of a Lévy process and its running extremum, which is more convenient for applications than general formulas in the first version of the paper. The derivation of explicit formulas in applications significantly simplifies.Under additional conditions, we derive analytical formulas using the Fourier/Laplace inversion and Wiener-Hopf factorization, and discuss efficient numerical methods for realization of these formulas. As applications, the cumulative probability distribution function of the process and its running maximum and the price of the option to exchange the maximum of a stock price for a power of the price are calculated. The most efficient numerical methods use the sinh-acceleration technique and simplified trapezoid rule. The program in Matlab running on a Mac with moderate characteristics achieves the precision E-7 and better in several milliseconds, and E-14 - in a fraction of a second.
Author | : Ditlev Monrad |
Publisher | : |
Total Pages | : 84 |
Release | : 1976 |
Genre | : |
ISBN | : |
Download Stable Lévy Processes Book in PDF, ePub and Kindle
Author | : Peter Mörters |
Publisher | : Cambridge University Press |
Total Pages | : |
Release | : 2010-03-25 |
Genre | : Mathematics |
ISBN | : 1139486578 |
Download Brownian Motion Book in PDF, ePub and Kindle
This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.
Author | : Andreas E. Kyprianou |
Publisher | : Springer Science & Business Media |
Total Pages | : 461 |
Release | : 2014-01-09 |
Genre | : Mathematics |
ISBN | : 3642376320 |
Download Fluctuations of Lévy Processes with Applications Book 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.
Author | : Roman Vershynin |
Publisher | : Cambridge University Press |
Total Pages | : 299 |
Release | : 2018-09-27 |
Genre | : Business & Economics |
ISBN | : 1108415199 |
Download High-Dimensional Probability Book in PDF, ePub and Kindle
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author | : Günter Last |
Publisher | : Cambridge University Press |
Total Pages | : 315 |
Release | : 2017-10-26 |
Genre | : Mathematics |
ISBN | : 1107088011 |
Download Lectures on the Poisson Process Book in PDF, ePub and Kindle
A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Author | : Peter Tankov |
Publisher | : CRC Press |
Total Pages | : 552 |
Release | : 2003-12-30 |
Genre | : Business & Economics |
ISBN | : 1135437947 |
Download Financial Modelling with Jump Processes Book 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
Author | : Jayakrishnan Nair |
Publisher | : Cambridge University Press |
Total Pages | : 266 |
Release | : 2022-06-09 |
Genre | : Mathematics |
ISBN | : 1009062964 |
Download The Fundamentals of Heavy Tails Book in PDF, ePub and Kindle
Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.
Author | : David Applebaum |
Publisher | : Cambridge University Press |
Total Pages | : 461 |
Release | : 2009-04-30 |
Genre | : Mathematics |
ISBN | : 1139477986 |
Download Lévy Processes and Stochastic Calculus Book in PDF, ePub and Kindle
Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.