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| Author | : Aleksand Janicki |
| Publisher | : CRC Press |
| Total Pages | : 378 |
| Release | : 2021-07-29 |
| Genre | : Mathematics |
| ISBN | : 1000447804 |
Presents new computer methods in approximation, simulation, and visualization for a host of alpha-stable stochastic processes.
| Author | : Ward Whitt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 616 |
| Release | : 2006-04-11 |
| Genre | : Mathematics |
| ISBN | : 0387217487 |
From the reviews: "The material is self-contained, but it is technical and a solid foundation in probability and queuing theory is beneficial to prospective readers. [... It] is intended to be accessible to those with less background. This book is a must to researchers and graduate students interested in these areas." ISI Short Book Reviews
| Author | : François G. Schmitt |
| Publisher | : Cambridge University Press |
| Total Pages | : 231 |
| Release | : 2016-01-07 |
| Genre | : Mathematics |
| ISBN | : 1107067618 |
This book provides a thorough understanding of the techniques used to retrieve multi-scale information from turbulent and complex systems, with case studies.
| Author | : Eckhard Platen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 868 |
| Release | : 2010-07-23 |
| Genre | : Mathematics |
| ISBN | : 364213694X |
In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.
| Author | : Gareth W. Peters |
| Publisher | : John Wiley & Sons |
| Total Pages | : 656 |
| Release | : 2015-05-05 |
| Genre | : Mathematics |
| ISBN | : 1118909550 |
A cutting-edge guide for the theories, applications, and statistical methodologies essential to heavy tailed risk modeling Focusing on the quantitative aspects of heavy tailed loss processes in operational risk and relevant insurance analytics, Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk presents comprehensive coverage of the latest research on the theories and applications in risk measurement and modeling techniques. Featuring a unique balance of mathematical and statistical perspectives, the handbook begins by introducing the motivation for heavy tailed risk processes in high consequence low frequency loss modeling. With a companion, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the book provides a complete framework for all aspects of operational risk management and includes: Clear coverage on advanced topics such as splice loss models, extreme value theory, heavy tailed closed form loss distributional approach models, flexible heavy tailed risk models, risk measures, and higher order asymptotic approximations of risk measures for capital estimation An exploration of the characterization and estimation of risk and insurance modelling, which includes sub-exponential models, alpha-stable models, and tempered alpha stable models An extended discussion of the core concepts of risk measurement and capital estimation as well as the details on numerical approaches to evaluation of heavy tailed loss process model capital estimates Numerous detailed examples of real-world methods and practices of operational risk modeling used by both financial and non-financial institutions Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk is an excellent reference for risk management practitioners, quantitative analysts, financial engineers, and risk managers. The book is also a useful handbook for graduate-level courses on heavy tailed processes, advanced risk management, and actuarial science.
| Author | : Joseph Klafter |
| Publisher | : World Scientific |
| Total Pages | : 530 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 9814340588 |
This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject. In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.
| Author | : Daniel Baier |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 372 |
| Release | : 2005-07-13 |
| Genre | : Mathematics |
| ISBN | : 9783540260073 |
It is a great privilege and pleasure to write a foreword for a book honor ing Wolfgang Gaul on the occasion of his sixtieth birthday. Wolfgang Gaul is currently Professor of Business Administration and Management Science and the Head of the Institute of Decision Theory and Management Science, Faculty of Economics, University of Karlsruhe (TH), Germany. He is, by any measure, one of the most distinguished and eminent scholars in the world today. Wolfgang Gaul has been instrumental in numerous leading research initia tives and has achieved an unprecedented level of success in facilitating com munication among researchers in diverse disciplines from around the world. A particularly remarkable and unique aspect of his work is that he has been a leading scholar in such diverse areas of research as graph theory and net work models, reliability theory, stochastic optimization, operations research, probability theory, sampling theory, cluster analysis, scaling and multivariate data analysis. His activities have been directed not only at these and other theoretical topics, but also at applications of statistical and mathematical tools to a multitude of important problems in computer science (e.g., w- mining), business research (e.g., market segmentation), management science (e.g., decision support systems) and behavioral sciences (e.g., preference mea surement and data mining). All of his endeavors have been accomplished at the highest level of professional excellence.
| Author | : Svetlozar T. Rachev |
| Publisher | : John Wiley & Sons |
| Total Pages | : 316 |
| Release | : 2011-02-08 |
| Genre | : Business & Economics |
| ISBN | : 0470937262 |
An in-depth guide to understanding probability distributions and financial modeling for the purposes of investment management In Financial Models with Lévy Processes and Volatility Clustering, the expert author team provides a framework to model the behavior of stock returns in both a univariate and a multivariate setting, providing you with practical applications to option pricing and portfolio management. They also explain the reasons for working with non-normal distribution in financial modeling and the best methodologies for employing it. The book's framework includes the basics of probability distributions and explains the alpha-stable distribution and the tempered stable distribution. The authors also explore discrete time option pricing models, beginning with the classical normal model with volatility clustering to more recent models that consider both volatility clustering and heavy tails. Reviews the basics of probability distributions Analyzes a continuous time option pricing model (the so-called exponential Lévy model) Defines a discrete time model with volatility clustering and how to price options using Monte Carlo methods Studies two multivariate settings that are suitable to explain joint extreme events Financial Models with Lévy Processes and Volatility Clustering is a thorough guide to classical probability distribution methods and brand new methodologies for financial modeling.
| Author | : Yisong Yang |
| Publisher | : World Scientific |
| Total Pages | : 371 |
| Release | : 2010 |
| Genre | : Science |
| ISBN | : 9814289302 |
Gun Shy
| Author | : Ole E Barndorff-Nielsen |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 324 |
| Release | : 2010-11-04 |
| Genre | : Business & Economics |
| ISBN | : 9813108002 |
Change of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law. Random change of time is key to understanding the nature of various stochastic processes, and gives rise to interesting mathematical results and insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, and also has a considerable role in insurance mathematics, large deviation theory, and other fields. The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance. It is invaluable as a textbook for graduate-level courses and students or a handy reference for researchers and practitioners in financial mathematics and econometrics.
