Download or read book Robust and Efficient Fitting of the Generalized Pareto Distribution with Actuarial Applications in View written by Vytaras Brazauskas and published by . This book was released on 2014 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to advances in extreme value theory, the generalized Pareto distribution (GPD) emerged as a natural family for modeling exceedances over a high threshold. Its importance in applications (e.g., insurance, finance, economics, engineering and numerous other fields) can hardly be overstated and is widely documented. However, despite the sound theoretical basis and wide applicability, fitting of this distribution in practice is not a trivial exercise. Traditional methods such as maximum likelihood and method-of-moments are undefined in some regions of the parameter space. Alternative approaches exist but they lack either robustness (e.g., probability-weighted moments) or efficiency (e.g., method-of-medians), or present significant numerical problems (e.g., minimum-divergence procedures). In this article, we propose a computationally tractable method for fitting the GPD, which is applicable for all parameter values and offers competitive trade-offs between robustness and efficiency. The method is based on 'trimmed moments'. Large-sample properties of the new estimators are provided, and their small-sample behavior under several scenarios of data contamination is investigated through simulations. We also study the effect of our methodology on actuarial applications. In particular, using the new approach, we fit the GPD to the Danish insurance data and apply the fitted model to a few risk measurement and ratemaking exercises.
Download or read book Issues in Insurance and Risk Management 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Insurance and Risk Management / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Insurance and Risk Management. The editors have built Issues in Insurance and Risk Management: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Insurance and Risk Management in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Insurance and Risk Management: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Download or read book Robust and Efficient Estimation for the Generalized Pareto Distribution written by Sergio Francisco Juʹarez and published by . This book was released on 2003 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Handbook of Graph Algorithms and Applications written by Krishnaiyan Thulasiraman and published by CRC Press. This book was released on 2015-05-12 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Graph Algorithms, Volume II : Applications focuses on a wide range of algorithmic applications, including graph theory problems. The book emphasizes new algorithms and approaches that have been triggered by applications. The approaches discussed require minimal exposure to related technologies in order to understand the material. Each chapter is devoted to a single application area, from VLSI circuits to optical networks to program graphs, and features an introduction by a pioneer researcher in that particular field. The book serves as a single-source reference for graph algorithms and their related applications.
Download or read book Actuarial Science written by Source Wikipedia and published by University-Press.org. This book was released on 2013-09 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 143. Chapters: Extreme value theory, Pareto distribution, Disease, Life expectancy, 100-year flood, Financial economics, Demography, Risk management, Discounting, Actuary, Value at risk, Time value of money, Workers' compensation, Regression analysis, Maximum life span, Enterprise risk management, Generalized linear model, Risk aversion, Copula, Reinsurance, Compound interest, Actuarial notation, Asset allocation, Medical underwriting, Wald's equation, Financial modeling, Life annuity, Retirement spend down, Failure rate, Stable and tempered stable distributions with volatility clustering - financial applications, Fictional actuaries, Mortality rate, Actuarial exam, RiskMetrics, Auto insurance risk selection, Model risk, Ulpian's life table, Coherent risk measure, Mathematical finance, Years of potential life lost, Ruin theory, Stochastic modelling, Insurance cycle, German Statutory Accident Insurance, Asset/liability modeling, Anders Lindstedt, Risk premium, Kaplan-Meier estimator, Lee-Carter Model, Worker's compensation, Mathematical statistics, Cresta, Catastrophe Risk Evaluating and Standardizing Target Accumulations, Actuarial present value, (a, b,0) class of distributions, Catastrophe modeling, Gompertz-Makeham law of mortality, Actuarial reserves, International Association of Black Actuaries, Compound annual growth rate, Liability-driven investment strategy, Decrement table, Risk modeling, Economic capital, Ogden tables, Financial engineering, John Graunt, Panjer recursion, Certified Risk Manager, Age stratification, Credibility theory, List of actuarial topics, Risk adjusted return on capital, De Moivre's law, Modeling and analysis of financial markets, Force of mortality, European Embedded Value, CAS Exam 7C 2009, Cohort, General insurance, Reliability theory, Tail value at risk, Insurable risk, Credit Valuation..
Download or read book Effective Statistical Learning Methods for Actuaries I written by Michel Denuit and published by Springer Nature. This book was released on 2019-09-03 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes the state of the art in generalized linear models (GLMs) and their various extensions: GAMs, mixed models and credibility, and some nonlinear variants (GNMs). In order to deal with tail events, analytical tools from Extreme Value Theory are presented. Going beyond mean modeling, it considers volatility modeling (double GLMs) and the general modeling of location, scale and shape parameters (GAMLSS). Actuaries need these advanced analytical tools to turn the massive data sets now at their disposal into opportunities. The exposition alternates between methodological aspects and case studies, providing numerical illustrations using the R statistical software. The technical prerequisites are kept at a reasonable level in order to reach a broad readership. This is the first of three volumes entitled Effective Statistical Learning Methods for Actuaries. Written by actuaries for actuaries, this series offers a comprehensive overview of insurance data analytics with applications to P&C, life and health insurance. Although closely related to the other two volumes, this volume can be read independently.
Download or read book Computational Actuarial Science with R written by Arthur Charpentier and published by CRC Press. This book was released on 2014-08-26 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Hands-On Approach to Understanding and Using Actuarial ModelsComputational Actuarial Science with R provides an introduction to the computational aspects of actuarial science. Using simple R code, the book helps you understand the algorithms involved in actuarial computations. It also covers more advanced topics, such as parallel computing and C/
Download or read book Actuarial Modelling of Extremal Events Using Transformed Generalized Extreme Value Distributions and Generalized Pareto Distributions written by Zhongxian Han and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: In 1928, Extreme Value Theory (EVT) originated in work of Fisher and Tippett describing the behavior of maximum of independent and identically distributed random variables. Various applications have been implemented successfully in many fields such as: actuarial science, hydrology, climatology, engineering, and economics and finance. This paper begins with introducing examples that extreme value theory comes to encounter. Then classical results from EVT are reviewed and the current research approaches are introduced. In particular, statistical methods are emphasized in detail for the modeling of extremal events. A case study of hurricane damages over the last century is presented using the "excess over threshold" (EOT) method. In most actual cases, the range of the data collected is finite with an upper bound while the fitted Generalized Extreme Value (GEV) and Generalized Pareto (GPD) distributions have infinite tails. Traditionally this is treated as trivial based on the assumption that the upper bound is so large that no significant result is affected when it is replaced by infinity. However, in certain circumstances, the models can be improved by implementing more specific techniques. Different transforms are introduced to rescale the GEV and GPD distributions so that they have finite supports. All classical methods can be applied directly to transformed models if the upper bound is known. In case the upper bound is unknown, we set up models with one additional parameter based on transformed distributions. Properties of the transform functions are studied and applied to find the cumulative density functions (cdfs) and probability density functions (pdfs) of the transformed distributions. We characterize the transformed distribution from the plots of their cdfs and mean residual life. Then we apply our findings to determine which transformed distribution should be used in the models. At the end some results of parameter estimation are obtained through the maximum likelihood method.
Download or read book Modeling Income Distributions and Lorenz Curves written by Duangkamon Chotikapanich and published by Springer Science & Business Media. This book was released on 2008-09-16 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jean-Jacques Rousseau wrote in the Preface to his famous Discourse on Inequality that “I consider the subject of the following discourse as one of the most interesting questions philosophy can propose, and unhappily for us, one of the most thorny that philosophers can have to solve. For how shall we know the source of inequality between men, if we do not begin by knowing mankind?” (Rousseau, 1754). This citation of Rousseau appears in an article in Spanish where Dagum (2001), in the memory of whom this book is published, also cites Socrates who said that the only useful knowledge is that which makes us better and Seneca who wrote that knowing what a straight line is, is not important if we do not know what rectitude is. These references are indeed a good illustration of Dagum’s vast knowledge, which was clearly not limited to the ?eld of Economics. For Camilo the ?rst part of Rousseau’s citation certainly justi?ed his interest in the ?eld of inequality which was at the centre of his scienti?c preoccupations. It should however be stressed that for Camilo the second part of the citation represented a “solid argument in favor of giving macroeconomic foundations to microeconomic behavior” (Dagum, 2001). More precisely, “individualism and methodological holism complete each other in contributing to the explanation of individual and social behavior” (Dagum, 2001).
Download or read book Loss Models written by Stuart A. Klugman and published by John Wiley & Sons. This book was released on 2012-01-25 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: An update of one of the most trusted books on constructing and analyzing actuarial models Written by three renowned authorities in the actuarial field, Loss Models, Third Edition upholds the reputation for excellence that has made this book required reading for the Society of Actuaries (SOA) and Casualty Actuarial Society (CAS) qualification examinations. This update serves as a complete presentation of statistical methods for measuring risk and building models to measure loss in real-world events. This book maintains an approach to modeling and forecasting that utilizes tools related to risk theory, loss distributions, and survival models. Random variables, basic distributional quantities, the recursive method, and techniques for classifying and creating distributions are also discussed. Both parametric and non-parametric estimation methods are thoroughly covered along with advice for choosing an appropriate model. Features of the Third Edition include: Extended discussion of risk management and risk measures, including Tail-Value-at-Risk (TVaR) New sections on extreme value distributions and their estimation Inclusion of homogeneous, nonhomogeneous, and mixed Poisson processes Expanded coverage of copula models and their estimation Additional treatment of methods for constructing confidence regions when there is more than one parameter The book continues to distinguish itself by providing over 400 exercises that have appeared on previous SOA and CAS examinations. Intriguing examples from the fields of insurance and business are discussed throughout, and all data sets are available on the book's FTP site, along with programs that assist with conducting loss model analysis. Loss Models, Third Edition is an essential resource for students and aspiring actuaries who are preparing to take the SOA and CAS preliminary examinations. It is also a must-have reference for professional actuaries, graduate students in the actuarial field, and anyone who works with loss and risk models in their everyday work. To explore our additional offerings in actuarial exam preparation visit www.wiley.com/go/actuarialexamprep.
Download or read book Statistical Size Distributions in Economics and Actuarial Sciences written by Christian Kleiber and published by John Wiley & Sons. This book was released on 2003-10-24 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive account of economic size distributions around the world and throughout the years In the course of the past 100 years, economists and applied statisticians have developed a remarkably diverse variety of income distribution models, yet no single resource convincingly accounts for all of these models, analyzing their strengths and weaknesses, similarities and differences. Statistical Size Distributions in Economics and Actuarial Sciences is the first collection to systematically investigate a wide variety of parametric models that deal with income, wealth, and related notions. Christian Kleiber and Samuel Kotz survey, compliment, compare, and unify all of the disparate models of income distribution, highlighting at times a lack of coordination between them that can result in unnecessary duplication. Considering models from eight languages and all continents, the authors discuss the social and economic implications of each as well as distributions of size of loss in actuarial applications. Specific models covered include: Pareto distributions Lognormal distributions Gamma-type size distributions Beta-type size distributions Miscellaneous size distributions Three appendices provide brief biographies of some of the leading players along with the basic properties of each of the distributions. Actuaries, economists, market researchers, social scientists, and physicists interested in econophysics will find Statistical Size Distributions in Economics and Actuarial Sciences to be a truly one-of-a-kind addition to the professional literature.
Download or read book Fitting Extreme Values Into Generalized Pareto Distribution written by GuiLi Liu and published by . This book was released on 2013 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistics of Extremes written by Jan Beirlant and published by John Wiley & Sons. This book was released on 2006-03-17 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.
Download or read book Generalized Linear Models for Insurance Data written by Piet de Jong and published by Cambridge University Press. This book was released on 2008-02-28 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the only book actuaries need to understand generalized linear models (GLMs) for insurance applications. GLMs are used in the insurance industry to support critical decisions. Until now, no text has introduced GLMs in this context or addressed the problems specific to insurance data. Using insurance data sets, this practical, rigorous book treats GLMs, covers all standard exponential family distributions, extends the methodology to correlated data structures, and discusses recent developments which go beyond the GLM. The issues in the book are specific to insurance data, such as model selection in the presence of large data sets and the handling of varying exposure times. Exercises and data-based practicals help readers to consolidate their skills, with solutions and data sets given on the companion website. Although the book is package-independent, SAS code and output examples feature in an appendix and on the website. In addition, R code and output for all the examples are provided on the website.
Download or read book Statistical and Probabilistic Methods in Actuarial Science written by Philip J. Boland and published by CRC Press. This book was released on 2007-03-05 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical and Probabilistic Methods in Actuarial Science covers many of the diverse methods in applied probability and statistics for students aspiring to careers in insurance, actuarial science, and finance. The book builds on students' existing knowledge of probability and statistics by establishing a solid and thorough understanding of
Download or read book Non Life Insurance Pricing with Generalized Linear Models written by Esbjörn Ohlsson and published by Springer Science & Business Media. This book was released on 2010-03-18 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-life insurance pricing is the art of setting the price of an insurance policy, taking into consideration varoius properties of the insured object and the policy holder. Introduced by British actuaries generalized linear models (GLMs) have become today a the standard aproach for tariff analysis. The book focuses on methods based on GLMs that have been found useful in actuarial practice and provides a set of tools for a tariff analysis. Basic theory of GLMs in a tariff analysis setting is presented with useful extensions of standarde GLM theory that are not in common use. The book meets the European Core Syllabus for actuarial education and is written for actuarial students as well as practicing actuaries. To support reader real data of some complexity are provided at www.math.su.se/GLMbook.
Download or read book Extremes and Related Properties of Random Sequences and Processes written by M. R. Leadbetter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.
