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Lundberg Approximations For Compound Distributions With Insurance Applications
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Book Synopsis Lundberg Approximations for Compound Distributions with Insurance Applications by : Gordon E Willmot
Download or read book Lundberg Approximations for Compound Distributions with Insurance Applications written by Gordon E Willmot and published by . This book was released on 2000-10-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lundberg Approximations for Compound Distributions with Insurance Applications by : Gordon E. Willmot
Download or read book Lundberg Approximations for Compound Distributions with Insurance Applications written by Gordon E. Willmot and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes represent our summary of much of the recent research that has been done in recent years on approximations and bounds that have been developed for compound distributions and related quantities which are of interest in insurance and other areas of application in applied probability. The basic technique employed in the derivation of many bounds is induc tive, an approach that is motivated by arguments used by Sparre-Andersen (1957) in connection with a renewal risk model in insurance. This technique is both simple and powerful, and yields quite general results. The bounds themselves are motivated by the classical Lundberg exponential bounds which apply to ruin probabilities, and the connection to compound dis tributions is through the interpretation of the ruin probability as the tail probability of a compound geometric distribution. The initial exponential bounds were given in Willmot and Lin (1994), followed by the nonexpo nential generalization in Willmot (1994). Other related work on approximations for compound distributions and applications to various problems in insurance in particular and applied probability in general is also discussed in subsequent chapters. The results obtained or the arguments employed in these situations are similar to those for the compound distributions, and thus we felt it useful to include them in the notes. In many cases we have included exact results, since these are useful in conjunction with the bounds and approximations developed.
Download or read book Loss Models written by Stuart A. Klugman and published by John Wiley & Sons. This book was released on 2013-08-05 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Surplus Analysis of Sparre Andersen Insurance Risk Processes by : Gordon E. Willmot
Download or read book Surplus Analysis of Sparre Andersen Insurance Risk Processes written by Gordon E. Willmot and published by Springer. This book was released on 2017-12-21 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This carefully written monograph covers the Sparre Andersen process in an actuarial context using the renewal process as the model for claim counts. A unified reference on Sparre Andersen (renewal risk) processes is included, often missing from existing literature. The authors explore recent results and analyse various risk theoretic quantities associated with the event of ruin, including the time of ruin and the deficit of ruin. Particular attention is given to the explicit identification of defective renewal equation components, which are needed to analyse various risk theoretic quantities and are also relevant in other subject areas of applied probability such as dams and storage processes, as well as queuing theory. Aimed at researchers interested in risk/ruin theory and related areas, this work will also appeal to graduate students in classical and modern risk theory and Gerber-Shiu analysis.
Book Synopsis Series Approximation Methods in Statistics by : John E. Kolassa
Download or read book Series Approximation Methods in Statistics written by John E. Kolassa and published by Springer Science & Business Media. This book was released on 2006-09-23 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised book presents theoretical results relevant to Edgeworth and saddlepoint expansions to densities and distribution functions. It provides examples of their application in some simple and a few complicated settings, along with numerical, as well as asymptotic, assessments of their accuracy. Variants on these expansions, including much of modern likelihood theory, are discussed and applications to lattice distributions are extensively treated.
Book Synopsis Closure Properties for Heavy-Tailed and Related Distributions by : Remigijus Leipus
Download or read book Closure Properties for Heavy-Tailed and Related Distributions written by Remigijus Leipus and published by Springer Nature. This book was released on 2023-10-16 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a compact and systematic overview of closure properties of heavy-tailed and related distributions, including closure under tail equivalence, convolution, finite mixing, maximum, minimum, convolution power and convolution roots, and product-convolution closure. It includes examples and counterexamples that give an insight into the theory and provides numerous references to technical details and proofs for a deeper study of the subject. The book will serve as a useful reference for graduate students, young researchers, and applied scientists.
Book Synopsis Data Analysis and Related Applications 4 by : Yiannis Dimotikalis
Download or read book Data Analysis and Related Applications 4 written by Yiannis Dimotikalis and published by John Wiley & Sons. This book was released on 2024-10-08 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Risk Measures and Insurance Solvency Benchmarks by : Vsevolod K. Malinovskii
Download or read book Risk Measures and Insurance Solvency Benchmarks written by Vsevolod K. Malinovskii and published by CRC Press. This book was released on 2021-07-22 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk Measures and Insurance Solvency Benchmarks: Fixed-Probability Levels in Renewal Risk Models is written for academics and practitioners who are concerned about potential weaknesses of the Solvency II regulatory system. It is also intended for readers who are interested in pure and applied probability, have a taste for classical and asymptotic analysis, and are motivated to delve into rather intensive calculations. The formal prerequisite for this book is a good background in analysis. The desired prerequisite is some degree of probability training, but someone with knowledge of the classical real-variable theory, including asymptotic methods, will also find this book interesting. For those who find the proofs too complicated, it may be reassuring that most results in this book are formulated in rather elementary terms. This book can also be used as reading material for basic courses in risk measures, insurance mathematics, and applied probability. The material of this book was partly used by the author for his courses in several universities in Moscow, Copenhagen University, and in the University of Montreal. Features Requires only minimal mathematical prerequisites in analysis and probability Suitable for researchers and postgraduate students in related fields Could be used as a supplement to courses in risk measures, insurance mathematics and applied probability.
Download or read book Actuarial Science written by Hanji Shang and published by World Scientific. This book was released on 2006 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since actuarial education was introduced into China in the 1980s, Chinese scholars have paid greater attention to the theoretical research of actuarial science. Professors and industry experts from well-known universities in China recently worked together on the project ?Insurance Information Processing and Actuarial Mathematics Theory and Methodology?, which was supported by the Chinese government. Summarizing what they achieved, this volume provides a study of some basic problems of actuarial science, including risk models, risk evaluation and analysis, and premium principles. The contributions cover some new applications of probability and statistics, fuzzy mathematics and financial economics to the field of actuarial practices. Discussions on the new insurance market in China are also presented.
Book Synopsis Benchmarking, Temporal Distribution, and Reconciliation Methods for Time Series by : Estela Bee Dagum
Download or read book Benchmarking, Temporal Distribution, and Reconciliation Methods for Time Series written by Estela Bee Dagum and published by Springer Science & Business Media. This book was released on 2006-09-23 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time series play a crucial role in modern economies at all levels of activity and are used by decision makers to plan for a better future. Before publication time series are subject to statistical adjustments and this is the first statistical book to systematically deal with the methods most often applied for such adjustments. Regression-based models are emphasized because of their clarity, ease of application, and superior results. Each topic is illustrated with real case examples. In order to facilitate understanding of their properties and limitations of the methods discussed a real data example is followed throughout the book.
Book Synopsis Space, Structure and Randomness by : Michel Bilodeau
Download or read book Space, Structure and Randomness written by Michel Bilodeau and published by Springer Science & Business Media. This book was released on 2007-12-23 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Space, structure, and randomness: these are the three key concepts underlying Georges Matheron’s scientific work. He first encountered them at the beginning of his career when working as a mining engineer, and then they resurfaced in fields ranging from meteorology to microscopy. What could these radically different types of applications possibly have in common? First, in each one only a single realisation of the phenomenon is available for study, but its features repeat themselves in space; second, the sampling pattern is rarely regular, and finally there are problems of change of scale. This volume is divided in three sections on random sets, geostatistics and mathematical morphology. They reflect his professional interests and his search for underlying unity. Some readers may be surprised to find theoretical chapters mixed with applied ones. We have done this deliberately. GM always considered that the distinction between the theory and practice was purely academic. When GM tackled practical problems, he used his skill as a physicist to extract the salient features and to select variables which could be measured meaningfully and whose values could be estimated from the available data. Then he used his outstanding ability as a mathematician to solve the problems neatly and efficiently. It was his capacity to combine a physicist’s intuition with a mathematician’s analytical skills that allowed him to produce new and innovative solutions to difficult problems. The book should appeal to graduate students and researchers working in mathematics, probability, statistics, physics, spatial data analysis, and image analysis. In addition it will be of interest to those who enjoy discovering links between scientific disciplines that seem unrelated at first glance. In writing the book the contributors have tried to put GM’s ideas into perspective. During his working life, GM was a genuinely creative scientist. He developed innovative concepts whose usefulness goes far beyond the confines of the discipline for which they were originally designed. This is why his work remains as pertinent today as it was when it was first written.
Book Synopsis Weak Dependence: With Examples and Applications by : Jérôme Dedecker
Download or read book Weak Dependence: With Examples and Applications written by Jérôme Dedecker and published by Springer Science & Business Media. This book was released on 2007-07-18 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops Doukhan/Louhichi's 1999 idea to measure asymptotic independence of a random process. The authors, who helped develop this theory, propose examples of models fitting such conditions: stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Applications are still needed to develop a method of analysis for nonlinear times series, and this book provides a strong basis for additional studies.
Book Synopsis Spatial Statistics: Methodological Aspects and Applications by : Marc Moore
Download or read book Spatial Statistics: Methodological Aspects and Applications written by Marc Moore and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains presentations by eminent researchers: Statistical Inference for Spatial Processes; Image Analysis; Applications of Spatial Statistics in Earth, Environmental, and Health Sciences; and Statistics of Brain Mapping. They range from asymptotic considerations for spatial processes to practical considerations related to particular applications including important methodological aspects. Many contributions concern image analysis, mainly images related to brain mapping.
Book Synopsis Nonparametric Monte Carlo Tests and Their Applications by : Li-Xing Zhu
Download or read book Nonparametric Monte Carlo Tests and Their Applications written by Li-Xing Zhu and published by Springer Science & Business Media. This book was released on 2005-08-09 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo approximation to the null distribution of the test provides a convenient means of testing model fit. This book proposes a Monte Carlo-based methodology to construct this type of approximation when the model is semistructured. It addresses both applied and theoretical aspects of nonparametric Monte Carlo tests.
Book Synopsis Copula Theory and Its Applications by : Piotr Jaworski
Download or read book Copula Theory and Its Applications written by Piotr Jaworski and published by Springer Science & Business Media. This book was released on 2010-07-16 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 50's, copulas have gained considerable popularity in several fields of applied mathematics, such as finance, insurance and reliability theory. Today, they represent a well-recognized tool for market and credit models, aggregation of risks, portfolio selection, etc. This book is divided into two main parts: Part I - "Surveys" contains 11 chapters that provide an up-to-date account of essential aspects of copula models. Part II - "Contributions" collects the extended versions of 6 talks selected from papers presented at the workshop in Warsaw.
Book Synopsis An Introduction to Copulas by : Roger B. Nelsen
Download or read book An Introduction to Copulas written by Roger B. Nelsen and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.
Book Synopsis Multivariate Dispersion, Central Regions, and Depth by : Karl Mosler
Download or read book Multivariate Dispersion, Central Regions, and Depth written by Karl Mosler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has many applications to stochastic comparison problems in economics and other fields. It covers theory of lift zonoids and demonstrates its usefulness in multivariate analysis, an informal introduction to basic ideas, and a comprehensive investigation into the theory, as well as various applications of the lift zonoid approach and may be separately studied. Readers are assumed to have a firm grounding in probability at the graduate level.
