Insurance Risk and Ruin


Book Description

The focus of this book is on the two major areas of risk theory: aggregate claims distributions and ruin theory. For aggregate claims distributions, detailed descriptions are given of recursive techniques that can be used in the individual and collective risk models. For the collective model, the book discusses different classes of counting distribution, and presents recursion schemes for probability functions and moments. For the individual model, the book illustrates the three most commonly applied techniques. Beyond the classical topics in ruin theory, this new edition features an expanded section covering time of ruin problems, Gerber–Shiu functions, and the application of De Vylder approximations. Suitable for a first course in insurance risk theory and extensively classroom tested, the book is accessible to readers with a solid understanding of basic probability. Numerous worked examples are included and each chapter concludes with exercises for which complete solutions are provided.




Nonlife Actuarial Models


Book Description

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




Collective Risk Models with Dependence


Book Description

In actuarial science, collective risk models, in which the aggregate claim amount of a portfolio is defined in terms of random sums, play a crucial role. In these models, it is common to assume that the number of claims and their amounts are independent, even if this might not always be the case. We consider collective risk models with different dependence structures. Due to the importance of such distributions in an actuarial setting, we first investigate a collective risk model with dependence involving the family of multivariate mixed Erlang distributions. Other models based on mixtures involving bivariate and multivariate copulas in a more general setting are then presented. These different structures allow to link the number of claims to each claim amount, and to quantify the aggregate claim loss. Then, we use Archimedean and hierarchical Archimedean copulas in collective risk models, to model the dependence between the claim number random variable and the claim amount random variables involved in the random sum. Such dependence structures allow us to derive a computational methodology for the assessment of the aggregate claim amount. While being very flexible, this methodology is easy to implement, and can easily fit more complicated hierarchical structures.




Collective Risk Models with Dependence Uncertainty


Book Description

We bring the recently developed framework of dependence uncertainty into collective risk models, one of the most classic models in actuarial science. We study the worst-case values of the Value-at-Risk (VaR) and the Expected Shortfall (ES) of the aggregate loss in collective risk models, under two settings of dependence uncertainty: (i) the counting random variable (claim frequency) and the individual losses (claim sizes) are independent, and the dependence of the individual losses is unknown; (ii) the dependence of the counting random variable and the individual losses is unknown. Analytical results for the worst-case values of ES are obtained. For the loss from a large portfolio of insurance policies, an asymptotic equivalence of VaR and ES is established. Our results can be used to provide approximations for VaR and ES in collective risk models with unknown dependence. Approximation errors are obtained in both cases.




Risk Theory


Book Description




Risk Modelling in General Insurance


Book Description

A wide range of topics give students a firm foundation in statistical and actuarial concepts and their applications.




Loss Models


Book Description

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.




Collective Risk Assessment in Affordable Care Act Markets


Book Description

The changes that the Affordable Care Act introduced to the US health insurance market have entirely altered the traditional ratemaking process. Precisely, the creation of statewide community rating schemes and a guaranteed issue has facilitated insurance coverage to the high-risk population, leading to massive changes in risk pool compositions. The implementation of Risk Adjustment has neutralized some of the consequences of limiting premium variation in the market. However, setting appropriate rate levels has remained cumbersome due to the uncertainty about the statewide risk pool. Many insurers, who could not quantify the health risk associated with the statewide yearly enrollment, had to face unexpectedly high payments on risk equalization. Natsis (2019) stated that in this environment, the use of traditional univariate techniques to project statewide health care costs could be potentially misleading. This thesis proposes a Bayesian approach to reflect important sources of uncertainty over statewide actuarial estimates. The aggregate loss is modeled with a novel collective risk model based on a Generalized Beta Prime (GBP) distribution, accounting for long tail risks and changes in risk pool compositions. The GBP is presented with a mean-dispersion parametrization, which allows the introduction of a hierarchical prior specification over the state-specific means. This parameter structure, responsible of quantifying uncertainty and sharing information among states, is a cornerstone of the adopted collective risk model. Using the Commercial Health Care data extract published by the Society of Actuaries (2019), the model is applied on the Surgical and Transplant service category. The resulting heavy-tailed posteriors of the nationwide service means illustrate the high variation of inpatient medical costs. Moreover, the posteriors of the statewide aggregate claims remain highly right-skewed, reflecting the risk of facing sicker populations and high-cost treatments at individual claim level.




Actuarial Loss Models


Book Description

Actuarial loss models are statistical models used by insurance companies to estimate the frequency and severity of future losses, set premiums, and reserve funds to cover potential claims. Actuarial loss models are a subject in actuarial mathematics that focus on the pricing and reserving for short-term coverages. This is a concise textbook written for undergraduate students majoring in actuarial science who wish to learn the basics of actuarial loss models. This book can be used as a textbook for a one-semester course on actuarial loss models. The prerequisite for this book is a first course on calculus. The reader is supposed to be familiar with differentiation and integration. This book covers part of the learning outcomes of the Fundamentals of Actuarial Mathematics (FAM) exam and the Advanced Short-Term Actuarial Mathematics (ASTAM) exam administered by the Society of Actuaries. It can be used by actuarial students and practitioners who prepare for the aforementioned actuarial exams. Key Features: Review core concepts in probability theory. Cover important topics in actuarial loss models. Include worked examples. Provide both theoretical and numerical exercises. Include solutions of selected exercises.