Point Processes with a Generalized Order Statistic Property PDF Download
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Author: Birgit Debrabant
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832519599
Category :
Languages : en
Pages : 154
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Book Description
Mixed Poisson processes are a well known class of point processes derived from (stationary) Poisson processes. In particular they cover cases where the intensity of a Poisson process is unknown but can be assumed to follow a known probability distribution. This situation is common e. g. in insurance mathematics where for instance the number of accident claims in which an individual is involved and which is evolving over some time can in principal be well described by a Poisson process with an individual, yet normally unknown intensity corresponding to the individual's accident proneness. Modelling this intensity as a random variable naturally leads to a mixed model. Usually, an insurance company will have a good estimate of the associated mixing distribution due to its large portfolio of policies.
Author: Birgit Debrabant
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832519599
Category :
Languages : en
Pages : 154
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Book Description
Mixed Poisson processes are a well known class of point processes derived from (stationary) Poisson processes. In particular they cover cases where the intensity of a Poisson process is unknown but can be assumed to follow a known probability distribution. This situation is common e. g. in insurance mathematics where for instance the number of accident claims in which an individual is involved and which is evolving over some time can in principal be well described by a Poisson process with an individual, yet normally unknown intensity corresponding to the individual's accident proneness. Modelling this intensity as a random variable naturally leads to a mixed model. Usually, an insurance company will have a good estimate of the associated mixing distribution due to its large portfolio of policies.
Author: Haijun Li
Publisher: Springer Science & Business Media
ISBN: 1461468922
Category : Mathematics
Languages : en
Pages : 459
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Book Description
Stochastic Orders in Reliability and Risk Management is composed of 19 contributions on the theory of stochastic orders, stochastic comparison of order statistics, stochastic orders in reliability and risk analysis, and applications. These review/exploratory chapters present recent and current research on stochastic orders reported at the International Workshop on Stochastic Orders in Reliability and Risk Management, or SORR2011, which took place in the City Hotel, Xiamen, China, from June 27 to June 29, 2011. The conference’s talks and invited contributions also represent the celebration of Professor Moshe Shaked, who has made comprehensive, fundamental contributions to the theory of stochastic orders and its applications in reliability, queueing modeling, operations research, economics and risk analysis. This volume is in honor of Professor Moshe Shaked. The work presented in this volume represents active research on stochastic orders and multivariate dependence, and exemplifies close collaborations between scholars working in different fields. The Xiamen Workshop and this volume seek to revive the community workshop tradition on stochastic orders and dependence and strengthen research collaboration, while honoring the work of a distinguished scholar.
Author: J Grandell
Publisher: CRC Press
ISBN: 1000109992
Category : Mathematics
Languages : en
Pages : 281
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Book Description
To date, Mixed Poisson processes have been studied by scientists primarily interested in either insurance mathematics or point processes. Work in one area has often been carried out without knowledge of the other area. Mixed Poisson Processes is the first book to combine and concentrate on these two themes, and to distinguish between the notions of distributions and processes. The first part of the text gives special emphasis to the estimation of the underlying intensity, thinning, infinite divisibility, and reliability properties. The second part is, to a greater extent, based on Lundberg's thesis.
Author: Thomas Mikosch
Publisher: Springer Science & Business Media
ISBN: 3540882332
Category : Mathematics
Languages : en
Pages : 435
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Book Description
"Offers a mathematical introduction to non-life insurance and, at the same time, to a multitude of applied stochastic processes. It gives detailed discussions of the fundamental models for claim sizes, claim arrivals, the total claim amount, and their probabilistic properties....The reader gets to know how the underlying probabilistic structures allow one to determine premiums in a portfolio or in an individual policy." --Zentralblatt für Didaktik der Mathematik
Author: North-Holland Publishing Company
Publisher:
ISBN:
Category :
Languages : en
Pages : 1216
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Book Description
Author: Alan Karr
Publisher: Routledge
ISBN: 1351423827
Category : Mathematics
Languages : en
Pages : 524
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Book Description
First Published in 2017. Routledge is an imprint of Taylor & Francis, an Informa company.
Author: Thorsten Wiegand
Publisher: CRC Press
ISBN: 142008254X
Category : Mathematics
Languages : en
Pages : 542
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Book Description
Understand How to Analyze and Interpret Information in Ecological Point Patterns Although numerous statistical methods for analyzing spatial point patterns have been available for several decades, they haven’t been extensively applied in an ecological context. Addressing this gap, Handbook of Spatial Point-Pattern Analysis in Ecology shows how the techniques of point-pattern analysis are useful for tackling ecological problems. Within an ecological framework, the book guides readers through a variety of methods for different data types and aids in the interpretation of the results obtained by point-pattern analysis. Ideal for empirical ecologists who want to avoid advanced theoretical literature, the book covers statistical techniques for analyzing and interpreting the information contained in ecological patterns. It presents methods used to extract information hidden in spatial point-pattern data that may point to the underlying processes. The authors focus on point processes and null models that have proven their immediate utility for broad ecological applications, such as cluster processes. Along with the techniques, the handbook provides a comprehensive selection of real-world examples. Most of the examples are analyzed using Programita, a continuously updated software package based on the authors’ many years of teaching and collaborative research in ecological point-pattern analysis. Programita is tailored to meet the needs of real-world applications in ecology. The software and a manual are available online.
Author: Stuart A. Klugman
Publisher: John Wiley & Sons
ISBN: 1118573749
Category : Business & Economics
Languages : en
Pages : 368
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Book Description
An essential resource for constructing and analyzing advanced actuarial models Loss Models: Further Topics presents extended coverage of modeling through the use of tools related to risk theory, loss distributions, and survival models. The book uses these methods to construct and evaluate actuarial models in the fields of insurance and business. Providing an advanced study of actuarial methods, the book features extended discussions of risk modeling and risk measures, including Tail-Value-at-Risk. Loss Models: Further Topics contains additional material to accompany the Fourth Edition of Loss Models: From Data to Decisions, such as: Extreme value distributions Coxian and related distributions Mixed Erlang distributions Computational and analytical methods for aggregate claim models Counting processes Compound distributions with time-dependent claim amounts Copula models Continuous time ruin models Interpolation and smoothing The book is an essential reference for practicing actuaries and actuarial researchers who want to go beyond the material required for actuarial qualification. Loss Models: Further Topics is also an excellent resource for graduate students in the actuarial field.
Author: Sidney I. Resnick
Publisher: Springer Science & Business Media
ISBN: 1461203872
Category : Mathematics
Languages : en
Pages : 640
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Book Description
Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. This text offers easy access to this fundamental topic for many students of applied sciences at many levels. It includes examples, exercises, applications, and computational procedures. It is uniquely useful for beginners and non-beginners in the field. No knowledge of measure theory is presumed.
Author: Anatoliy Swishchuk
Publisher: CRC Press
ISBN: 1000776816
Category : Mathematics
Languages : en
Pages : 289
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Book Description
Stochastic Modelling of Big Data in Finance provides a rigorous overview and exploration of stochastic modelling of big data in finance (BDF). The book describes various stochastic models, including multivariate models, to deal with big data in finance. This includes data in high-frequency and algorithmic trading, specifically in limit order books (LOB), and shows how those models can be applied to different datasets to describe the dynamics of LOB, and to figure out which model is the best with respect to a specific data set. The results of the book may be used to also solve acquisition, liquidation and market making problems, and other optimization problems in finance. Features Self-contained book suitable for graduate students and post-doctoral fellows in financial mathematics and data science, as well as for practitioners working in the financial industry who deal with big data All results are presented visually to aid in understanding of concepts Dr. Anatoliy Swishchuk is a Professor in Mathematical Finance at the Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada. He got his B.Sc. and M.Sc. degrees from Kyiv State University, Kyiv, Ukraine. He earned two doctorate degrees in Mathematics and Physics (PhD and DSc) from the prestigious National Academy of Sciences of Ukraine (NASU), Kiev, Ukraine, and is a recipient of NASU award for young scientist with a gold medal for series of research publications in random evolutions and their applications. Dr. Swishchuk is a chair and organizer of finance and energy finance seminar ‘Lunch at the Lab’ at the Department of Mathematics and Statistics. Dr. Swishchuk is a Director of Mathematical and Computational Finance Laboratory at the University of Calgary. He was a steering committee member of the Professional Risk Managers International Association (PRMIA), Canada (2006-2015), and is a steering committee member of Global Association of Risk Professionals (GARP), Canada (since 2015). Dr. Swishchuk is a creator of mathematical finance program at the Department of Mathematics & Statistics. He is also a proponent for a new specialization “Financial and Energy Markets Data Modelling” in the Data Science and Analytics program. His research areas include financial mathematics, random evolutions and their applications, biomathematics, stochastic calculus, and he serves on editorial boards for four research journals. He is the author of more than 200 publications, including 15 books and more than 150 articles in peer-reviewed journals. In 2018 he received a Peak Scholar award.
