Structured Dependence between Stochastic Processes
Structured Dependence between Stochastic Processes

Author: Tomasz R. Bielecki

Publisher: Cambridge University Press

Published: 2020-08-27

Total Pages: 280

ISBN-13: 1108895379

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The relatively young theory of structured dependence between stochastic processes has many real-life applications in areas including finance, insurance, seismology, neuroscience, and genetics. With this monograph, the first to be devoted to the modeling of structured dependence between random processes, the authors not only meet the demand for a solid theoretical account but also develop a stochastic processes counterpart of the classical copula theory that exists for finite-dimensional random variables. Presenting both the technical aspects and the applications of the theory, this is a valuable reference for researchers and practitioners in the field, as well as for graduate students in pure and applied mathematics programs. Numerous theoretical examples are included, alongside examples of both current and potential applications, aimed at helping those who need to model structured dependence between dynamic random phenomena.

Credit Correlation
Credit Correlation

Author: Youssef Elouerkhaoui

Publisher: Springer

Published: 2017-11-15

Total Pages: 466

ISBN-13: 3319609734

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This book provides an advanced guide to correlation modelling for credit portfolios, providing both theoretical underpinnings and practical implementation guidance. The book picks up where pre-crisis credit books left off, offering guidance for quants on the latest tools and techniques for credit portfolio modelling in the presence of CVA (Credit Value Adjustments). Written at an advanced level, it assumes that readers are familiar with the fundamentals of credit modelling covered, for example, in the market leading books by Schonbucher (2003) and O’Kane (2008). Coverage will include the latest default correlation approaches; correlation modelling in the ‘Marshall-Olkin’ contagion framework, in the context of CVA; numerical implementation; and pricing, calibration and risk challenges. The explosive growth of credit derivatives markets in the early-to-mid 000’s was bought to a close by the 2007 financial crisis, where these instruments were held largely to blame for the economic downturn. However, in the wake of increased regulation across all financial instruments and the challenge of buying and selling bonds in large amounts, credit derivatives have once again been found to be the answer and the market has grown significantly. Written by a practitioner for practitioners, this book will also interest researchers in mathematical finance who want to understand how things happen and work ‘on the floor’. Building the reader’s knowledge from the ground up, and with numerous real life examples used throughout, this book will prove a popular reference for anyone with a mathematical mind interested credit markets.

Highly Structured Stochastic Systems
Highly Structured Stochastic Systems

Author: Peter J. Green

Publisher:

Published: 2003

Total Pages: 536

ISBN-13: 9780198510550

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Through this text, the author aims to make recent developments in the title subject (a modern strategy for the creation of statistical models to solve 'real world' problems) accessible to graduate students and researchers in the field of statistics.

Dependence in Probability and Statistics
Dependence in Probability and Statistics

Author: Paul Doukhan

Publisher: Springer Science & Business Media

Published: 2010-07-23

Total Pages: 222

ISBN-13: 3642141048

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This account of recent works on weakly dependent, long memory and multifractal processes introduces new dependence measures for studying complex stochastic systems and includes other topics such as the dependence structure of max-stable processes.

Empirical Process Techniques for Dependent Data
Empirical Process Techniques for Dependent Data

Author: Herold Dehling

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 378

ISBN-13: 1461200997

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Empirical process techniques for independent data have been used for many years in statistics and probability theory. These techniques have proved very useful for studying asymptotic properties of parametric as well as non-parametric statistical procedures. Recently, the need to model the dependence structure in data sets from many different subject areas such as finance, insurance, and telecommunications has led to new developments concerning the empirical distribution function and the empirical process for dependent, mostly stationary sequences. This work gives an introduction to this new theory of empirical process techniques, which has so far been scattered in the statistical and probabilistic literature, and surveys the most recent developments in various related fields. Key features: A thorough and comprehensive introduction to the existing theory of empirical process techniques for dependent data * Accessible surveys by leading experts of the most recent developments in various related fields * Examines empirical process techniques for dependent data, useful for studying parametric and non-parametric statistical procedures * Comprehensive bibliographies * An overview of applications in various fields related to empirical processes: e.g., spectral analysis of time-series, the bootstrap for stationary sequences, extreme value theory, and the empirical process for mixing dependent observations, including the case of strong dependence. To date this book is the only comprehensive treatment of the topic in book literature. It is an ideal introductory text that will serve as a reference or resource for classroom use in the areas of statistics, time-series analysis, extreme value theory, point process theory, and applied probability theory. Contributors: P. Ango Nze, M.A. Arcones, I. Berkes, R. Dahlhaus, J. Dedecker, H.G. Dehling,

Stochastic Models of Structural Plasma Turbulence
Stochastic Models of Structural Plasma Turbulence

Author: Victor Yu Korolev

Publisher: Walter de Gruyter

Published: 2006

Total Pages: 424

ISBN-13: 9789067644495

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The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.

Exponential Families of Stochastic Processes
Exponential Families of Stochastic Processes

Author: Uwe Küchler

Publisher: Springer Science & Business Media

Published: 2006-05-09

Total Pages: 325

ISBN-13: 0387227652

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A comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors - two of the leading experts in the field - and several other researchers. The theory is applied to a broad spectrum of examples, covering a large number of frequently applied stochastic process models with discrete as well as continuous time. To make the reading even easier for statisticians with only a basic background in the theory of stochastic process, the first part of the book is based on classical theory of stochastic processes only, while stochastic calculus is used later. Most of the concepts and tools from stochastic calculus needed when working with inference for stochastic processes are introduced and explained without proof in an appendix. This appendix can also be used independently as an introduction to stochastic calculus for statisticians. Numerous exercises are also included.

Dependence Modeling Between Continuous Time Stochastic Processes
Dependence Modeling Between Continuous Time Stochastic Processes

Author: Thomas Deschatre

Publisher:

Published: 2017

Total Pages: 213

ISBN-13:

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In this thesis, we study some dependence modeling problems between continuous time stochastic processes. These results are applied to the modeling and risk management of electricity markets. In a first part, we propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. We show that the class of admissible copulae for the Brownian motions contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. Results are applied to the joint modeling of electricity and other energy commodity prices. In a second part, we consider a stochastic process which is a sum of a continuous semimartingale and a mean reverting compound Poisson process and which is discretely observed. An estimation procedure is proposed for the mean reversion parameter of the Poisson process in a high frequency framework with finite time horizon, assuming this parameter is large. Results are applied to the modeling of the spikes in electricity prices time series. In a third part, we consider a doubly stochastic Poisson process with stochastic intensity function of a continuous semimartingale. A local polynomial estimator is considered in order to infer the intensity function and a method is given to select the optimal bandwidth. An oracle inequality is derived. Furthermore, a test is proposed in order to determine if the intensity function belongs to some parametrical family. Using these results, we model the dependence between the intensity of electricity spikes and exogenous factors such as the wind production.