Lundberg Approximations For Compound Distributions With Insurance Applications
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Lundberg Approximations For Compound Distributions With Insurance Applications
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Author : Gordon E Willmot
language : en
Publisher:
Release Date : 2000-10-01
Lundberg Approximations For Compound Distributions With Insurance Applications written by Gordon E Willmot and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-01 with categories.
Lundberg Approximations For Compound Distributions With Insurance Applications
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Author : Gordon E. Willmot
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lundberg Approximations For Compound Distributions With Insurance Applications written by Gordon E. Willmot 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.
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.
Lundberg Approximations For Compound Distributions With Insurance Applications
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Author : Gordon E. Willmot
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Lundberg Approximations For Compound Distributions With Insurance Applications written by Gordon E. Willmot 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 2001 with Business & Economics categories.
This monograph discusses Lundberg approximations for compound distributions with special emphasis on applications in insurance risk modeling. These distributions are somewhat awkward from an analytic standpoint, but play a central role in insurance and other areas of applied probability modeling such as queueing theory. Consequently, the material is of interest to researchers and graduate students interested in these areas. The material is self-contained, but an introductory course in insurance risk theory is beneficial to prospective readers. Lundberg asymptotics and bounds have a long history in connection with ruin probabilities and waiting time distributions in queueing theory, and have more recently been extended to compound distributions. This connection has its roots in the compound geometric representation of the ruin probabilities and waiting time distributions. A systematic treatment of these approximations is provided, drawing heavily on monotonicity ideas from reliability theory. The results are then applied to the solution of defective renewal equations, analysis of the time and severity of insurance ruin, and renewal risk models, which may also be viewed in terms of the equilibrium waiting time distribution in the G/G/1 queue. Many known results are derived and extended so that much of the material has not appeared elsewhere in the literature. A unique feature involves the use of elementary analytic techniques which require only undergraduate mathematics as a prerequisite. New proofs of many results are given, and an extensive bibliography is provided. Gordon Willmot is Professor of Statistics and Actuarial Science at the University of Waterloo. His research interests are in insurance risk and queueing theory. He is an associate editor of the North American Actuarial Journal.
Loss Models
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Author : Stuart A. Klugman
language : en
Publisher: John Wiley & Sons
Release Date : 2013-08-05
Loss Models written by Stuart A. Klugman and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-05 with Business & Economics categories.
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.
Surplus Analysis Of Sparre Andersen Insurance Risk Processes
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Author : Gordon E. Willmot
language : en
Publisher: Springer
Release Date : 2017-12-21
Surplus Analysis Of Sparre Andersen Insurance Risk Processes written by Gordon E. Willmot and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-21 with Business & Economics categories.
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.
Series Approximation Methods In Statistics
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Author : John E. Kolassa
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-23
Series Approximation Methods In Statistics written by John E. Kolassa 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 2006-09-23 with Mathematics categories.
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.
Closure Properties For Heavy Tailed And Related Distributions
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Author : Remigijus Leipus
language : en
Publisher: Springer Nature
Release Date : 2023-09-14
Closure Properties For Heavy Tailed And Related Distributions written by Remigijus Leipus and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-14 with Mathematics categories.
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.
Actuarial Science
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Author : Hanji Shang
language : en
Publisher: World Scientific
Release Date : 2006
Actuarial Science written by Hanji Shang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
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.
Benchmarking Temporal Distribution And Reconciliation Methods For Time Series
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Author : Estela Bee Dagum
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-23
Benchmarking Temporal Distribution And Reconciliation Methods For Time Series written by Estela Bee Dagum 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 2006-09-23 with Business & Economics categories.
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.
Risk Measures And Insurance Solvency Benchmarks
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Author : Vsevolod K. Malinovskii
language : en
Publisher: CRC Press
Release Date : 2021-07-21
Risk Measures And Insurance Solvency Benchmarks written by Vsevolod K. Malinovskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-21 with Business & Economics categories.
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.