Claim Models

This collection of articles addresses the most modern forms of loss reserving methodology: granular models and machine learning models. New methodologies come with questions about their applicability. These questions are discussed in one article, which focuses on the relative merits of granular and machine learning models. Others illustrate applications with real-world data. The examples include neural networks, which, though well known in some disciplines, have previously been limited in the actuarial literature. This volume expands on that literature, with specific attention to their application to loss reserving. For example, one of the articles introduces the application of neural networks of the gated recurrent unit form to the actuarial literature, whereas another uses a penalized neural network. Neural networks are not the only form of machine learning, and two other papers outline applications of gradient boosting and regression trees respectively. Both articles construct loss reserves at the individual claim level so that these models resemble granular models. One of these articles provides a practical application of the model to claim watching, the action of monitoring claim development and anticipating major features. Such watching can be used as an early warning system or for other administrative purposes. Overall, this volume is an extremely useful addition to the libraries of those working at the loss reserving frontier.

There are a wide range of variables for actuaries to consider when calculating a motorist’s insurance premium, such as age, gender and type of vehicle. Further to these factors, motorists’ rates are subject to experience rating systems, including credibility mechanisms and Bonus Malus systems (BMSs). Actuarial Modelling of Claim Counts presents a comprehensive treatment of the various experience rating systems and their relationships with risk classification. The authors summarize the most recent developments in the field, presenting ratemaking systems, whilst taking into account exogenous information. The text: Offers the first self-contained, practical approach to a priori and a posteriori ratemaking in motor insurance. Discusses the issues of claim frequency and claim severity, multi-event systems, and the combinations of deductibles and BMSs. Introduces recent developments in actuarial science and exploits the generalised linear model and generalised linear mixed model to achieve risk classification. Presents credibility mechanisms as refinements of commercial BMSs. Provides practical applications with real data sets processed with SAS software. Actuarial Modelling of Claim Counts is essential reading for students in actuarial science, as well as practicing and academic actuaries. It is also ideally suited for professionals involved in the insurance industry, applied mathematicians, quantitative economists, financial engineers and statisticians.

This class-tested undergraduate textbook covers the entire syllabus for Exam C of the Society of Actuaries (SOA).

This practical introduction outlines methods for analysing actuarial and financial risk at a fairly elementary mathematical level suitable for graduate students, actuaries and other analysts in the industry who could use simulation as a problem solver. Numerous exercises with R-code illustrate the text.

This collection of articles addresses the most modern forms of loss reserving methodology: granular models and machine learning models. New methodologies come with questions about their applicability. These questions are discussed in one article, which focuses on the relative merits of granular and machine learning models. Others illustrate applications with real-world data. The examples include neural networks, which, though well known in some disciplines, have previously been limited in the actuarial literature. This volume expands on that literature, with specific attention to their application to loss reserving. For example, one of the articles introduces the application of neural networks of the gated recurrent unit form to the actuarial literature, whereas another uses a penalized neural network. Neural networks are not the only form of machine learning, and two other papers outline applications of gradient boosting and regression trees respectively. Both articles construct loss reserves at the individual claim level so that these models resemble granular models. One of these articles provides a practical application of the model to claim watching, the action of monitoring claim development and anticipating major features. Such watching can be used as an early warning system or for other administrative purposes. Overall, this volume is an extremely useful addition to the libraries of those working at the loss reserving frontier.

Most insurers around the world have introduced some form of merit-rating in automobile third party liability insurance. Such systems, penalizing at-fault accidents by premium surcharges and rewarding claim-free years by discounts, are called bonus-malus systems (BMS) in Europe and Asia. With the current deregulation trends that concern most insurance markets around the world, many companies will need to develop their own BMS. The main objective of the book is to provide them models to design BMS that meet their objectives. Part I of the book contains an overall presentation of the pros and cons of merit-rating, a case study and a review of the different probability distributions that can be used to model the number of claims in an automobile portfolio. In Part II, 30 systems from 22 different countries, are evaluated and ranked according to their `toughness' towards policyholders. Four tools are created to evaluate that toughness and provide a tentative classification of all systems. Then, factor analysis is used to aggregate and summarize the data, and provide a final ranking of all systems. Part III is an up-to-date review of all the probability models that have been proposed for the design of an optimal BMS. The application of these models would enable the reader to devise the system that is ideally suited to the behavior of the policyholders of his own insurance company. Finally, Part IV analyses an alternative to BMS; the introduction of a policy with a deductible.

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.

The volume presents innovations in data analysis and classification and gives an overview of the state of the art in these scientific fields and applications. Areas that receive considerable attention in the book are discrimination and clustering, data analysis and statistics, as well as applications in marketing, finance, and medicine. The reader will find material on recent technical and methodological developments and a large number of applications demonstrating the usefulness of the newly developed techniques.

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.