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Introductory Lectures On Fluctuations Of Levy Processes With Applications
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Book Synopsis Introductory Lectures on Fluctuations of Lévy Processes with Applications by : Andreas E. Kyprianou
Download or read book Introductory Lectures on Fluctuations of Lévy Processes with Applications written by Andreas E. Kyprianou and published by Springer Science & Business Media. This book was released on 2006-12-18 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fluctuations of Lévy Processes with Applications by : Andreas E. Kyprianou
Download or read book Fluctuations of Lévy Processes with Applications written by Andreas E. Kyprianou and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fluctuations of Levy Processes with Applications by : Andreas E. Kyprianou
Download or read book Fluctuations of Levy Processes with Applications written by Andreas E. Kyprianou and published by . This book was released on 2014-01-31 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fluctuation Theory for Lévy Processes by : Ronald A. Doney
Download or read book Fluctuation Theory for Lévy Processes written by Ronald A. Doney and published by Springer. This book was released on 2007-04-25 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lévy processes, that is, processes in continuous time with stationary and independent increments, form a flexible class of models, which have been applied to the study of storage processes, insurance risk, queues, turbulence, laser cooling, and of course finance, where they include particularly important examples having "heavy tails." Their sample path behaviour poses a variety of challenging and fascinating problems, which are addressed in detail.
Book Synopsis Queues and Lévy Fluctuation Theory by : Krzysztof Dębicki
Download or read book Queues and Lévy Fluctuation Theory written by Krzysztof Dębicki and published by Springer. This book was released on 2015-08-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an extensive introduction to queueing models driven by Lévy-processes as well as a systematic account of the literature on Lévy-driven queues. The objective is to make the reader familiar with the wide set of probabilistic techniques that have been developed over the past decades, including transform-based techniques, martingales, rate-conservation arguments, change-of-measure, importance sampling, and large deviations. On the application side, it demonstrates how Lévy traffic models arise when modelling current queueing-type systems (as communication networks) and includes applications to finance. Queues and Lévy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.
Book Synopsis Lévy Processes and Stochastic Calculus by : David Applebaum
Download or read book Lévy Processes and Stochastic Calculus written by David Applebaum and published by Cambridge University Press. This book was released on 2009-04-30 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fully revised and appended edition of this unique volume, which develops together these two important subjects.
Book Synopsis Seminar on Stochastic Analysis, Random Fields and Applications VI by : Robert Dalang
Download or read book Seminar on Stochastic Analysis, Random Fields and Applications VI written by Robert Dalang and published by Springer Science & Business Media. This book was released on 2011-03-16 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains refereed research or review papers presented at the 6th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, in May 2008. The seminar focused mainly on stochastic partial differential equations, especially large deviations and control problems, on infinite dimensional analysis, particle systems and financial engineering, especially energy markets and climate models. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance.
Book Synopsis Séminaire de Probabilités LI by : Catherine Donati-Martin
Download or read book Séminaire de Probabilités LI written by Catherine Donati-Martin and published by Springer Nature. This book was released on 2022-05-13 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a selection of texts that reflects the current research streams in probability, with an interest toward topics such as filtrations, Markov processes and Markov chains as well as large deviations, Stochastic Partial Differential equations, rough paths theory, quantum probabilities and percolation on graphs. The featured contributors are R. L. Karandikar and B. V. Rao, C. Leuridan, M. Vidmar, L. Miclo and P. Patie, A. Bernou, M.-E. Caballero and A. Rouault, J. Dedecker, F. Merlevède and E. Rio, F. Brosset, T. Klein, A. Lagnoux and P. Petit, C. Marinelli and L. Scarpa, C. Castaing, N. Marie and P. Raynaud de Fitte, S. Attal, J. Deschamps and C. Pellegrini, and N. Eisenbaum.
Book Synopsis A Lifetime of Excursions Through Random Walks and Lévy Processes by : Loïc Chaumont
Download or read book A Lifetime of Excursions Through Random Walks and Lévy Processes written by Loïc Chaumont and published by Springer Nature. This book was released on 2022-01-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection honours Ron Doney’s work and includes invited articles by his collaborators and friends. After an introduction reviewing Ron Doney’s mathematical achievements and how they have influenced the field, the contributed papers cover both discrete-time processes, including random walks and variants thereof, and continuous-time processes, including Lévy processes and diffusions. A good number of the articles are focused on classical fluctuation theory and its ramifications, the area for which Ron Doney is best known.
Book Synopsis Levy Processes in Credit Risk by : Wim Schoutens
Download or read book Levy Processes in Credit Risk written by Wim Schoutens and published by John Wiley & Sons. This book was released on 2010-06-15 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory guide to using Lévy processes for credit risk modelling. It covers all types of credit derivatives: from the single name vanillas such as Credit Default Swaps (CDSs) right through to structured credit risk products such as Collateralized Debt Obligations (CDOs), Constant Proportion Portfolio Insurances (CPPIs) and Constant Proportion Debt Obligations (CPDOs) as well as new advanced rating models for Asset Backed Securities (ABSs). Jumps and extreme events are crucial stylized features, essential in the modelling of the very volatile credit markets - the recent turmoil in the credit markets has once again illustrated the need for more refined models. Readers will learn how the classical models (driven by Brownian motions and Black-Scholes settings) can be significantly improved by using the more flexible class of Lévy processes. By doing this, extreme event and jumps can be introduced into the models to give more reliable pricing and a better assessment of the risks. The book brings in high-tech financial engineering models for the detailed modelling of credit risk instruments, setting up the theoretical framework behind the application of Lévy Processes to Credit Risk Modelling before moving on to the practical implementation. Complex credit derivatives structures such as CDOs, ABSs, CPPIs, CPDOs are analysed and illustrated with market data.
Book Synopsis Pricing Derivatives Under Lévy Models by : Andrey Itkin
Download or read book Pricing Derivatives Under Lévy Models written by Andrey Itkin and published by Birkhäuser. This book was released on 2017-02-27 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary. The latter part of the book demonstrates the efficacy of the method by solving some typical problems encountered in computational finance, including structural default models with jumps, and local stochastic volatility models with stochastic interest rates and jumps. The author also adds extra complexity to the traditional statements of these problems by taking into account jumps in each stochastic component while all jumps are fully correlated, and shows how this setting can be efficiently addressed within the framework of the new method. Written for non-mathematicians, this book will appeal to financial engineers and analysts, econophysicists, and researchers in applied numerical analysis. It can also be used as an advance course on modern finite-difference methods or computational finance.
Book Synopsis XII Symposium of Probability and Stochastic Processes by : Daniel Hernández-Hernández
Download or read book XII Symposium of Probability and Stochastic Processes written by Daniel Hernández-Hernández and published by Springer. This book was released on 2018-06-26 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the XII Symposium of Probability and Stochastic Processes which took place at Universidad Autonoma de Yucatan in Merida, Mexico, on November 16–20, 2015. This meeting was the twelfth meeting in a series of ongoing biannual meetings aimed at showcasing the research of Mexican probabilists as well as promote new collaborations between the participants. The book features articles drawn from different research areas in probability and stochastic processes, such as: risk theory, limit theorems, stochastic partial differential equations, random trees, stochastic differential games, stochastic control, and coalescence. Two of the main manuscripts survey recent developments on stochastic control and scaling limits of Markov-branching trees, written by Kazutoshi Yamasaki and Bénédicte Haas, respectively. The research-oriented manuscripts provide new advances in active research fields in Mexico. The wide selection of topics makes the book accessible to advanced graduate students and researchers in probability and stochastic processes.
Book Synopsis Advanced Mathematical Methods for Finance by : Julia Di Nunno
Download or read book Advanced Mathematical Methods for Finance written by Julia Di Nunno and published by Springer Science & Business Media. This book was released on 2011-03-29 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.
Book Synopsis The Cramér–Lundberg Model and Its Variants by : Michel Mandjes
Download or read book The Cramér–Lundberg Model and Its Variants written by Michel Mandjes and published by Springer Nature. This book was released on 2023-12-29 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive examination of the Cramér–Lundberg model, which is the most extensively researched model in ruin theory. It covers the fundamental dynamics of an insurance company's surplus level in great detail, presenting a thorough analysis of the ruin probability and related measures for both the standard model and its variants. Providing a systematic and self-contained approach to evaluate the crucial quantities found in the Cramér–Lundberg model, the book makes use of connections with related queueing models when appropriate, and its emphasis on clean transform-based techniques sets it apart from other works. In addition to consolidating a wealth of existing results, the book also derives several new outcomes using the same methodology. This material is complemented by a thoughtfully chosen collection of exercises. The book's primary target audience is master's and starting PhD students in applied mathematics, operations research, and actuarial science, although it also serves as a useful methodological resource for more advanced researchers. The material is self-contained, requiring only a basic grounding in probability theory and some knowledge of transform techniques.
Book Synopsis Applied Modeling Techniques and Data Analysis 2 by : Yannis Dimotikalis
Download or read book Applied Modeling Techniques and Data Analysis 2 written by Yannis Dimotikalis and published by John Wiley & Sons. This book was released on 2021-03-26 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: BIG DATA, ARTIFICIAL INTELLIGENCE AND DATA ANALYSIS SET Coordinated by Jacques Janssen Data analysis is a scientific field that continues to grow enormously, most notably over the last few decades, following rapid growth within the tech industry, as well as the wide applicability of computational techniques alongside new advances in analytic tools. Modeling enables data analysts to identify relationships, make predictions, and to understand, interpret and visualize the extracted information more strategically. This book includes the most recent advances on this topic, meeting increasing demand from wide circles of the scientific community. Applied Modeling Techniques and Data Analysis 2 is a collective work by a number of leading scientists, analysts, engineers, mathematicians and statisticians, working on the front end of data analysis and modeling applications. The chapters cover a cross section of current concerns and research interests in the above scientific areas. The collected material is divided into appropriate sections to provide the reader with both theoretical and applied information on data analysis methods, models and techniques, along with appropriate applications.
Book Synopsis Lévy Processes and Their Applications in Reliability and Storage by : Mohamed Abdel-Hameed
Download or read book Lévy Processes and Their Applications in Reliability and Storage written by Mohamed Abdel-Hameed and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers Lévy processes and their applications in the contexts of reliability and storage. Special attention is paid to life distributions and the maintenance of devices subject to degradation; estimating the parameters of the degradation process is also discussed, as is the maintenance of dams subject to Lévy input.
Book Synopsis Stochastic Analysis for Poisson Point Processes by : Giovanni Peccati
Download or read book Stochastic Analysis for Poisson Point Processes written by Giovanni Peccati and published by Springer. This book was released on 2016-07-07 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets.
