Filtering And Parameter Estimation For Partially Observed Generalized Hawkes Processes
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Filtering And Parameter Estimation For Partially Observed Generalized Hawkes Processes
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Author : Anca Patricia Vacarescu
language : en
Publisher: Stanford University
Release Date : 2011
Filtering And Parameter Estimation For Partially Observed Generalized Hawkes Processes written by Anca Patricia Vacarescu and has been published by Stanford University this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
We consider the nonlinear filtering problem for partially observed Generalized Hawkes Processes, which can be applied in the context of portfolio credit risk. The problem belongs to the larger class of hidden Markov models, where the counting process is observed at discrete points in time and the observations are sparse, while the intensity driving process in unobservable. We construct the conditional distribution of the process given the information filtration and we discuss the analytical and numerical properties of the corresponding filters. In particular, we study the sensitivity of the filters with respect to the parameters of the model, and we obtain a monotonicity result with respect to the jump and the volatility terms driving the intensity. Using the scaled process, we provide necessary and sufficient conditions for the frequency of time observations in terms of the parameters of the model, to ensure a good performance of the filter. We also address the problem of parameter estimation for the Generalized Hawkes Process in the framework of the EM algorithm, and we analyze the effect of the self-exciting feature of our process on the asymptotic and numerical properties of the estimators.
Filtering And Parameter Estimation For Partially Observed Generalized Hawkes Processes
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Author : Anca Patricia Vacarescu
language : en
Publisher:
Release Date : 2011
Filtering And Parameter Estimation For Partially Observed Generalized Hawkes Processes written by Anca Patricia Vacarescu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
We consider the nonlinear filtering problem for partially observed Generalized Hawkes Processes, which can be applied in the context of portfolio credit risk. The problem belongs to the larger class of hidden Markov models, where the counting process is observed at discrete points in time and the observations are sparse, while the intensity driving process in unobservable. We construct the conditional distribution of the process given the information filtration and we discuss the analytical and numerical properties of the corresponding filters. In particular, we study the sensitivity of the filters with respect to the parameters of the model, and we obtain a monotonicity result with respect to the jump and the volatility terms driving the intensity. Using the scaled process, we provide necessary and sufficient conditions for the frequency of time observations in terms of the parameters of the model, to ensure a good performance of the filter. We also address the problem of parameter estimation for the Generalized Hawkes Process in the framework of the EM algorithm, and we analyze the effect of the self-exciting feature of our process on the asymptotic and numerical properties of the estimators.
Fundamentals Of The Theory Of Structured Dependence Between Stochastic Processes
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Author : Tomasz R. Bielecki
language : en
Publisher: Cambridge University Press
Release Date : 2020-08-27
Fundamentals Of The Theory Of Structured Dependence Between Stochastic Processes written by Tomasz R. Bielecki and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-27 with Business & Economics categories.
Comprehensive presentation of the technical aspects and applications of the theory of structured dependence between random processes.
Current Index To Statistics Applications Methods And Theory
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Author :
language : en
Publisher:
Release Date : 1997
Current Index To Statistics Applications Methods And Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematical statistics categories.
The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
The Elements Of Hawkes Processes
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Author : Patrick J. Laub
language : en
Publisher: Springer Nature
Release Date : 2022-01-03
The Elements Of Hawkes Processes written by Patrick J. Laub and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-03 with Mathematics categories.
Hawkes processes are studied and used in a wide range of disciplines: mathematics, social sciences, and earthquake modelling, to name a few. This book presents a selective coverage of the core and recent topics in the broad field of Hawkes processes. It consists of three parts. Parts I and II summarise and provide an overview of core theory (including key simulation methods) and inference methods, complemented by a selection of recent research developments and applications. Part III is devoted to case studies in seismology and finance that connect the core theory and inference methods to practical scenarios. This book is designed primarily for applied probabilists, statisticians, and machine learners. However, the mathematical prerequisites have been kept to a minimum so that the content will also be of interest to undergraduates in advanced mathematics and statistics, as well as machine learning practitioners. Knowledge of matrix theory with basics of probability theory, including Poisson processes, is considered a prerequisite. Colour-blind-friendly illustrations are included.
Index To Theses With Abstracts Accepted For Higher Degrees By The Universities Of Great Britain And Ireland And The Council For National Academic Awards
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Author :
language : en
Publisher:
Release Date : 2008
Index To Theses With Abstracts Accepted For Higher Degrees By The Universities Of Great Britain And Ireland And The Council For National Academic Awards written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Dissertations, Academic categories.
Aspects Of Risk Theory
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Author : Jan Grandell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Aspects Of Risk Theory written by Jan Grandell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Risk theory, which deals with stochastic models of an insurance business, is a classical application of probability theory. The fundamental problem in risk theory is to investigate the ruin possibility of the risk business. Traditionally the occurrence of the claims is described by a Poisson process and the cost of the claims by a sequence of random variables. This book is a treatise of risk theory with emphasis on models where the occurrence of the claims is described by more general point processes than the Poisson process, such as renewal processes, Cox processes and general stationary point processes. In the Cox case the possibility of risk fluctuation is explicitly taken into account. The presentation is based on modern probabilistic methods rather than on analytic methods. The theory is accompanied with discussions on practical evaluation of ruin probabilities and statistical estimation. Many numerical illustrations of the results are given.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2003
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Random Processes For Engineers
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Author : Bruce Hajek
language : en
Publisher: Cambridge University Press
Release Date : 2015-03-12
Random Processes For Engineers written by Bruce Hajek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-12 with Computers categories.
An engaging introduction to the critical tools needed to design and evaluate engineering systems operating in uncertain environments.
Statistics Subject Indexes From Mathematical Reviews
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Author : American Mathematical Society
language : en
Publisher:
Release Date : 1987
Statistics Subject Indexes From Mathematical Reviews written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.