Statistical and Probabilistic Methods in Actuarial Science

Author: Philip J. Boland

Publisher: CRC Press

ISBN: 158488696X

Category: Mathematics

Page: 368

View: 7224

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 these methods. It also emphasizes the wide variety of practical situations in insurance and actuarial science where these techniques may be used. Although some chapters are linked, several can be studied independently from the others. The first chapter introduces claims reserving via the deterministic chain ladder technique. The next few chapters survey loss distributions, risk models in a fixed period of time, and surplus processes, followed by an examination of credibility theory in which collateral and sample information are brought together to provide reasonable methods of estimation. In the subsequent chapter, experience rating via no claim discount schemes for motor insurance provides an interesting application of Markov chain methods. The final chapters discuss generalized linear models and decision and game theory. Developed by an author with many years of teaching experience, this text presents an accessible, sound foundation in both the theory and applications of actuarial science. It encourages students to use the statistical software package R to check examples and solve problems.
Posted in Mathematics

Risk Analysis in Finance and Insurance, Second Edition

Author: Alexander Melnikov

Publisher: CRC Press

ISBN: 1420070525

Category: Mathematics

Page: 328

View: 2602

Risk Analysis in Finance and Insurance, Second Edition presents an accessible yet comprehensive introduction to the main concepts and methods that transform risk management into a quantitative science. Taking into account the interdisciplinary nature of risk analysis, the author discusses many important ideas from mathematics, finance, and actuarial science in a simplified manner. He explores the interconnections among these disciplines and encourages readers toward further study of the subject. This edition continues to study risks associated with financial and insurance contracts, using an approach that estimates the value of future payments based on current financial, insurance, and other information. New to the Second Edition Expanded section on the foundations of probability and stochastic analysis Coverage of new topics, including financial markets with stochastic volatility, risk measures, risk-adjusted performance measures, and equity-linked insurance More worked examples and problems Reorganized and expanded, this updated book illustrates how to use quantitative methods of stochastic analysis in modern financial mathematics. These methods can be naturally extended and applied in actuarial science, thus leading to unified methods of risk analysis and management.
Posted in Mathematics

Correspondence Analysis in Practice, Third Edition

Author: Michael Greenacre

Publisher: CRC Press

ISBN: 1315352958

Category: Mathematics

Page: 326

View: 7275

Drawing on the author’s 45 years of experience in multivariate analysis, Correspondence Analysis in Practice, Third Edition, shows how the versatile method of correspondence analysis (CA) can be used for data visualization in a wide variety of situations. CA and its variants, subset CA, multiple CA and joint CA, translate two-way and multi-way tables into more readable graphical forms — ideal for applications in the social, environmental and health sciences, as well as marketing, economics, linguistics, archaeology, and more. Michael Greenacre is Professor of Statistics at the Universitat Pompeu Fabra, Barcelona, Spain, where he teaches a course, amongst others, on Data Visualization. He has authored and co-edited nine books and 80 journal articles and book chapters, mostly on correspondence analysis, the latest being Visualization and Verbalization of Data in 2015. He has given short courses in fifteen countries to environmental scientists, sociologists, data scientists and marketing professionals, and has specialized in statistics in ecology and social science.
Posted in Mathematics

Analysis of Capture-Recapture Data

Author: Rachel S. McCrea,Byron J. T. Morgan

Publisher: CRC Press

ISBN: 1439836590

Category: Mathematics

Page: 314

View: 3701

An important first step in studying the demography of wild animals is to identify the animals uniquely through applying markings, such as rings, tags, and bands. Once the animals are encountered again, researchers can study different forms of capture-recapture data to estimate features, such as the mortality and size of the populations. Capture-recapture methods are also used in other areas, including epidemiology and sociology. With an emphasis on ecology, Analysis of Capture-Recapture Data covers many modern developments of capture-recapture and related models and methods and places them in the historical context of research from the past 100 years. The book presents both classical and Bayesian methods. A range of real data sets motivates and illustrates the material and many examples illustrate biometry and applied statistics at work. In particular, the authors demonstrate several of the modeling approaches using one substantial data set from a population of great cormorants. The book also discusses which computer programs to use for implementing the models and contains 130 exercises that extend the main material. The data sets, computer programs, and other ancillaries are available at www.capturerecapture.co.uk. The book is accessible to advanced undergraduate and higher-level students, quantitative ecologists, and statisticians. It helps readers understand model formulation and applications, including the technicalities of model diagnostics and checking.
Posted in Mathematics

Modern Directional Statistics

Author: Christophe Ley,Thomas Verdebout

Publisher: CRC Press

ISBN: 1351645781

Category: Computers

Page: 176

View: 1136

Modern Directional Statistics collects important advances in methodology and theory for directional statistics over the last two decades. It provides a detailed overview and analysis of recent results that can help both researchers and practitioners. Knowledge of multivariate statistics eases the reading but is not mandatory. The field of directional statistics has received a lot of attention over the past two decades, due to new demands from domains such as life sciences or machine learning, to the availability of massive data sets requiring adapted statistical techniques, and to technological advances. This book covers important progresses in distribution theory,high-dimensional statistics, kernel density estimation, efficient inference on directional supports, and computational and graphical methods. Christophe Ley is professor of mathematical statistics at Ghent University. His research interests include semi-parametrically efficient inference, flexible modeling, directional statistics and the study of asymptotic approximations via Stein’s Method. His achievements include the Marie-Jeanne Laurent-Duhamel prize of the Société Française de Statistique and an elected membership at the International Statistical Institute. He is associate editor for the journals Computational Statistics & Data Analysis and Econometrics and Statistics. Thomas Verdebout is professor of mathematical statistics at Université libre de Bruxelles (ULB). His main research interests are semi-parametric statistics, high- dimensional statistics, directional statistics and rank-based procedures. He has won an annual prize of the Belgian Academy of Sciences and is an elected member of the International Statistical Institute. He is associate editor for the journals Statistics and Probability Letters and Journal of Multivariate Analysis.
Posted in Computers

Bayesian Disease Mapping

Hierarchical Modeling in Spatial Epidemiology, Second Edition

Author: Andrew B. Lawson

Publisher: CRC Press

ISBN: 1466504811

Category: Mathematics

Page: 396

View: 6617

Since the publication of the first edition, many new Bayesian tools and methods have been developed for space-time data analysis, the predictive modeling of health outcomes, and other spatial biostatistical areas. Exploring these new developments, Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology, Second Edition provides an up-to-date, cohesive account of the full range of Bayesian disease mapping methods and applications. A biostatistics professor and WHO advisor, the author illustrates the use of Bayesian hierarchical modeling in the geographical analysis of disease through a range of real-world datasets. New to the Second Edition Three new chapters on regression and ecological analysis, putative hazard modeling, and disease map surveillance Expanded material on case event modeling and spatiotemporal analysis New and updated examples Two new appendices featuring examples of integrated nested Laplace approximation (INLA) and conditional autoregressive (CAR) models In addition to these new topics, the book covers more conventional areas such as relative risk estimation, clustering, spatial survival analysis, and longitudinal analysis. After an introduction to Bayesian inference, computation, and model assessment, the text focuses on important themes, including disease map reconstruction, cluster detection, regression and ecological analysis, putative hazard modeling, analysis of multiple scales and multiple diseases, spatial survival and longitudinal studies, spatiotemporal methods, and map surveillance. It shows how Bayesian disease mapping can yield significant insights into georeferenced health data. WinBUGS and R are used throughout for data manipulation and simulation.
Posted in Mathematics

Financial and Actuarial Statistics

An Introduction, Second Edition

Author: Dale S. Borowiak,Arnold F. Shapiro

Publisher: CRC Press

ISBN: 0203911245

Category: Mathematics

Page: 392

View: 7413

Understand Up-to-Date Statistical Techniques for Financial and Actuarial Applications Since the first edition was published, statistical techniques, such as reliability measurement, simulation, regression, and Markov chain modeling, have become more prominent in the financial and actuarial industries. Consequently, practitioners and students must acquire strong mathematical and statistical backgrounds in order to have successful careers. Financial and Actuarial Statistics: An Introduction, Second Edition enables readers to obtain the necessary mathematical and statistical background. It also advances the application and theory of statistics in modern financial and actuarial modeling. Like its predecessor, this second edition considers financial and actuarial modeling from a statistical point of view while adding a substantial amount of new material. New to the Second Edition Nomenclature and notations standard to the actuarial field Excel exercises with solutions, which demonstrate how to use Excel functions for statistical and actuarial computations Problems dealing with standard probability and statistics theory, along with detailed equation links A chapter on Markov chains and actuarial applications Expanded discussions of simulation techniques and applications, such as investment pricing Sections on the maximum likelihood approach to parameter estimation as well as asymptotic applications Discussions of diagnostic procedures for nonnegative random variables and Pareto, lognormal, Weibull, and left truncated distributions Expanded material on surplus models and ruin computations Discussions of nonparametric prediction intervals, option pricing diagnostics, variance of the loss function associated with standard actuarial models, and Gompertz and Makeham distributions Sections on the concept of actuarial statistics for a collection of stochastic status models The book presents a unified approach to both financial and actuarial modeling through the use of general status structures. The authors define future time-dependent financial actions in terms of a status structure that may be either deterministic or stochastic. They show how deterministic status structures lead to classical interest and annuity models, investment pricing models, and aggregate claim models. They also employ stochastic status structures to develop financial and actuarial models, such as surplus models, life insurance, and life annuity models.
Posted in Mathematics

Modern Actuarial Theory and Practice, Second Edition

Author: Philip Booth,Robert Chadburn,Steven Haberman,Dewi James,Zaki Khorasanee,Robert H. Plumb,Ben Rickayzen

Publisher: CRC Press

ISBN: 9781584883685

Category: Mathematics

Page: 840

View: 1730

In the years since the publication of the best-selling first edition, the incorporation of ideas and theories from the rapidly growing field of financial economics has precipitated considerable development of thinking in the actuarial profession. Modern Actuarial Theory and Practice, Second Edition integrates those changes and presents an up-to-date, comprehensive overview of UK and international actuarial theory, practice and modeling. It describes all of the traditional areas of actuarial activity, but in a manner that highlights the fundamental principles of actuarial theory and practice as well as their economic, financial, and statistical foundations.
Posted in Mathematics

A Course on Statistics for Finance

Author: Stanley L. Sclove

Publisher: CRC Press

ISBN: 1498785670

Category: Business & Economics

Page: 269

View: 8923

Taking a data-driven approach, A Course on Statistics for Finance presents statistical methods for financial investment analysis. The author introduces regression analysis, time series analysis, and multivariate analysis step by step using models and methods from finance. The book begins with a review of basic statistics, including descriptive statistics, kinds of variables, and types of data sets. It then discusses regression analysis in general terms and in terms of financial investment models, such as the capital asset pricing model and the Fama/French model. It also describes mean-variance portfolio analysis and concludes with a focus on time series analysis. Providing the connection between elementary statistics courses and quantitative finance courses, this text helps both existing and future quants improve their data analysis skills and better understand the modeling process.
Posted in Business & Economics

The Handbook of Graph Algorithms and Applications

Applications

Author: Krishnaiyan Thulasiraman,Arun Kumar Somani,Sarma Vrudhula

Publisher: CRC Press

ISBN: 1482227061

Category: Mathematics

Page: 1024

View: 5393

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.
Posted in Mathematics

Design and Analysis of Quality of Life Studies in Clinical Trials, Second Edition

Author: Diane L. Fairclough

Publisher: CRC Press

ISBN: 1420061186

Category: Mathematics

Page: 424

View: 9481

Design Principles and Analysis Techniques for HRQoL Clinical Trials SAS, R, and SPSS examples realistically show how to implement methods Focusing on longitudinal studies, Design and Analysis of Quality of Life Studies in Clinical Trials, Second Edition addresses design and analysis aspects in enough detail so that readers can apply statistical methods, such as mixed effect models, to their own studies. The author illustrates the implementation of the methods using the statistical software packages SAS, SPSS, and R. New to the Second Edition Data sets available for download online, allowing readers to replicate the analyses presented in the text New chapter on testing models that involve moderation and mediation Revised discussions of multiple comparisons procedures that focus on the integration of health-related quality of life (HRQoL) outcomes with other study outcomes using gatekeeper strategies Recent methodological developments for the analysis of trials with missing data New chapter on quality adjusted life-years (QALYs) and QTWiST specific to clinical trials Additional examples of the implementation of basic models and other selected applications in R and SPSS This edition continues to provide practical information for researchers directly involved in the design and analysis of HRQoL studies as well as for those who evaluate the design and interpret the results of HRQoL research. By following the examples in the book, readers will be able to apply the steps to their own trials.
Posted in Mathematics

Equity-Linked Life Insurance

Partial Hedging Methods

Author: Alexander Melnikov,Amir Nosrati

Publisher: CRC Press

ISBN: 1351644793

Category: Business & Economics

Page: 202

View: 7872

This book focuses on the application of the partial hedging approach from modern math finance to equity-linked life insurance contracts. It provides an accessible, up-to-date introduction to quantifying financial and insurance risks. The book also explains how to price innovative financial and insurance products from partial hedging perspectives. Each chapter presents the problem, the mathematical formulation, theoretical results, derivation details, numerical illustrations, and references to further reading.
Posted in Business & Economics

Claims Reserving in General Insurance

Author: David Hindley

Publisher: Cambridge University Press

ISBN: 1108514847

Category: Mathematics

Page: N.A

View: 987

This is a comprehensive and accessible reference source that documents the theoretical and practical aspects of all the key deterministic and stochastic reserving methods that have been developed for use in general insurance. Worked examples and mathematical details are included, along with many of the broader topics associated with reserving in practice. The key features of reserving in a range of different contexts in the UK and elsewhere are also covered. The book contains material that will appeal to anyone with an interest in claims reserving. It can be used as a learning resource for actuarial students who are studying the relevant parts of their professional bodies' examinations, as well as by others who are new to the subject. More experienced insurance and other professionals can use the book to refresh or expand their knowledge in any of the wide range of reserving topics covered in the book.
Posted in Mathematics

Pension Fund Risk Management

Financial and Actuarial Modeling

Author: Marco Micocci,Greg N. Gregoriou,Giovanni Batista Masala

Publisher: CRC Press

ISBN: 1439817545

Category: Business & Economics

Page: 764

View: 7181

As pension fund systems decrease and dependency ratios increase, risk management is becoming more complex in public and private pension plans. Pension Fund Risk Management: Financial and Actuarial Modeling sheds new light on the current state of pension fund risk management and provides new technical tools for addressing pension risk from an integrated point of view. Divided into four parts, the book first presents the correct measurement of risk in pension funds, fund dynamics under a performance-oriented arrangement, an attribution model for monitoring the performance and risk of a defined benefit (DB) pension fund, and an optimal investment problem of a defined contribution (DC) pension fund under inflationary risk. It also describes a pension plan from a dynamic optimization viewpoint, the optimal asset allocation of U.S. pension funds, the identification of stakeholders’ risks, value-at-risk (VaR) methodology, and various effects on the asset allocation of DB pension schemes. The second section focuses on the effects of uncertainty on employer-provided DB private pension plan liabilities; wage-based lump sum payments by death, retirement, or dismissal by the employer; fundamental retirement changes; occupational pension insurance in Germany; and longevity risk securitization in pension schemes. In the third part, the book examines employers’ risks, accountability rules and regulations, useful actuarial analysis instruments, risk-based solvency regime in the Netherlands, and the impact of the 2008 global financial crisis on pension participants. The final part covers DB pension freezes and terminations of plans, the two-pillar social security system of Italy, the Greek social security system, the effect of a company’s unfunded pension liabilities on its stock market valuation, and the returns of Spanish balanced pension plans and portfolio performance. With contributions from well-known, international academics and professionals, this book will assist pension fund executives, risk managers, consultants, and academic researchers in attaining a clear picture of the integration of risks in the pension world. It offers a comprehensive, contemporary account of how to handle the risks involved with pension funds.
Posted in Business & Economics

Statistical Size Distributions in Economics and Actuarial Sciences

Author: Christian Kleiber,Samuel Kotz

Publisher: John Wiley & Sons

ISBN: 9780471457169

Category: Mathematics

Page: 352

View: 6252

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.
Posted in Mathematics

Probability and Stochastic Modeling

Author: Vladimir I. Rotar

Publisher: CRC Press

ISBN: 1439872066

Category: Mathematics

Page: 508

View: 1004

A First Course in Probability with an Emphasis on Stochastic Modeling Probability and Stochastic Modeling not only covers all the topics found in a traditional introductory probability course, but also emphasizes stochastic modeling, including Markov chains, birth-death processes, and reliability models. Unlike most undergraduate-level probability texts, the book also focuses on increasingly important areas, such as martingales, classification of dependency structures, and risk evaluation. Numerous examples, exercises, and models using real-world data demonstrate the practical possibilities and restrictions of different approaches and help students grasp general concepts and theoretical results. The text is suitable for majors in mathematics and statistics as well as majors in computer science, economics, finance, and physics. The author offers two explicit options to teaching the material, which is reflected in "routes" designated by special "roadside" markers. The first route contains basic, self-contained material for a one-semester course. The second provides a more complete exposition for a two-semester course or self-study.
Posted in Mathematics

Nonparametric Curve Estimation

Methods, Theory, and Applications

Author: Sam Efromovich

Publisher: Springer Science & Business Media

ISBN: 0387226389

Category: Mathematics

Page: 414

View: 2829

This book gives a systematic, comprehensive, and unified account of modern nonparametric statistics of density estimation, nonparametric regression, filtering signals, and time series analysis. The companion software package, available over the Internet, brings all of the discussed topics into the realm of interactive research. Virtually every claim and development mentioned in the book is illustrated with graphs which are available for the reader to reproduce and modify, making the material fully transparent and allowing for complete interactivity.
Posted in Mathematics

Meta-analysis of Binary Data Using Profile Likelihood

Author: Dankmar Bohning,Sasivimol Rattanasiri,Ronny Kuhnert

Publisher: CRC Press

ISBN: 9781420011333

Category: Mathematics

Page: 208

View: 5562

Providing reliable information on an intervention effect, meta-analysis is a powerful statistical tool for analyzing and combining results from individual studies. Meta-Analysis of Binary Data Using Profile Likelihood focuses on the analysis and modeling of a meta-analysis with individually pooled data (MAIPD). It presents a unifying approach to modeling a treatment effect in a meta-analysis of clinical trials with binary outcomes. After illustrating the meta-analytic situation of an MAIPD with several examples, the authors introduce the profile likelihood model and extend it to cope with unobserved heterogeneity. They describe elements of log-linear modeling, ways for finding the profile maximum likelihood estimator, and alternative approaches to the profile likelihood method. The authors also discuss how to model covariate information and unobserved heterogeneity simultaneously and use the profile likelihood method to estimate odds ratios. The final chapters look at quantifying heterogeneity in an MAIPD and show how meta-analysis can be applied to the surveillance of scrapie. Containing new developments not available in the current literature, along with easy-to-follow inferences and algorithms, this book enables clinicians to efficiently analyze MAIPDs.
Posted in Mathematics

Statistical Methods in Healthcare

Author: Frederick Faltin,Ron S. Kenett,Fabrizio Ruggeri

Publisher: John Wiley & Sons

ISBN: 1119942047

Category: Medical

Page: 520

View: 6671

In recent years the number of innovative medicinal products and devices submitted and approved by regulatory bodies has declined dramatically. The medical product development process is no longer able to keep pace with increasing technologies, science and innovations and the goal is to develop new scientific and technical tools and to make product development processes more efficient and effective. Statistical Methods in Healthcare focuses on the application of statistical methodologies to evaluate promising alternatives and to optimize the performance and demonstrate the effectiveness of those that warrant pursuit is critical to success. Statistical methods used in planning, delivering and monitoring health care, as well as selected statistical aspects of the development and/or production of pharmaceuticals and medical devices are also addressed. With a focus on finding solutions to these challenges, this book: Provides a comprehensive, in-depth treatment of statistical methods in healthcare, along with a reference source for practitioners and specialists in health care and drug development. Offers a broad coverage of standards and established methods through leading edge techniques. Uses an integrated, case-study based approach, with focus on applications. Looks at the use of analytical and monitoring schemes to evaluate therapeutic performance. Features the application of modern quality management systems to clinical practice, and to pharmaceutical development and production processes. Addresses the use of modern Statistical methods such as Adaptive Design, Seamless Design, Data Mining, Bayesian networks and Bootstrapping that can be applied to support the challenging new vision. Practitioners in healthcare-related professions, ranging from clinical trials to care delivery to medical device design, as well as statistical researchers in the field, will benefit from this book.
Posted in Medical

Applied Bayesian Modelling

Author: Peter Congdon

Publisher: Wiley

ISBN: 9780471486954

Category: Mathematics

Page: 478

View: 4812

The use of Bayesian statistics has grown significantly in recent years, and will undoubtedly continue to do so. Applied Bayesian Modelling is the follow-up to the author’s best selling book, Bayesian Statistical Modelling, and focuses on the potential applications of Bayesian techniques in a wide range of important topics in the social and health sciences. The applications are illustrated through many real-life examples and software implementation in WINBUGS – a popular software package that offers a simplified and flexible approach to statistical modelling. The book gives detailed explanations for each example – explaining fully the choice of model for each particular problem. The book · Provides a broad and comprehensive account of applied Bayesian modelling. · Describes a variety of model assessment methods and the flexibility of Bayesian prior specifications. · Covers many application areas, including panel data models, structural equation and other multivariate structure models, spatial analysis, survival analysis and epidemiology. · Provides detailed worked examples in WINBUGS to illustrate the practical application of the techniques described. All WINBUGS programs are available from an ftp site. The book provides a good introduction to Bayesian modelling and data analysis for a wide range of people involved in applied statistical analysis, including researchers and students from statistics, and the health and social sciences. The wealth of examples makes this book an ideal reference for anyone involved in statistical modelling and analysis.
Posted in Mathematics