Download or read book The Collective Risk Model for Aggregate Losses written by Zhi Hu and published by . This book was released on 1999 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlife Actuarial Models written by Yiu-Kuen Tse and published by Cambridge University Press. This book was released on 2009-09-17 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This class-tested undergraduate textbook covers the entire syllabus for Exam C of the Society of Actuaries (SOA).
Download or read book Collective Risk Models with Dependence Uncertainty written by Haiyan Liu and published by . This book was released on 2017 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Collective Risk Models with Dependence written by Hélène Cossette and published by . This book was released on 2018 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Risk Modelling in General Insurance written by Roger J. Gray and published by Cambridge University Press. This book was released on 2012-06-28 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wide range of topics give students a firm foundation in statistical and actuarial concepts and their applications.
Download or read book Insurance Risk and Ruin written by David C. M. Dickson and published by Cambridge University Press. This book was released on 2016-10-27 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Risk Theory written by Hanspeter Schmidli and published by Springer. This book was released on 2018-04-04 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of classical actuarial techniques, including material that is not readily accessible elsewhere such as the Ammeter risk model and the Markov-modulated risk model. Other topics covered include utility theory, credibility theory, claims reserving and ruin theory. The author treats both theoretical and practical aspects and also discusses links to Solvency II. Written by one of the leading experts in the field, these lecture notes serve as a valuable introduction to some of the most frequently used methods in non-life insurance. They will be of particular interest to graduate students, researchers and practitioners in insurance, finance and risk management.
Download or read book Risk Theory written by and published by . This book was released on 1982 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Actuarial Loss Models written by Guojun Gan and published by CRC Press. This book was released on 2024-10-15 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Risk Models and Their Estimation written by Stephen G. Kellison and published by ACTEX Publications. This book was released on 2011 with total page 1150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much of actuarial science deals with the analysis and management of financial risk. In this text we address the topic of loss models, traditionally called risk theory by actuaries, including the estimation of such models from sample data. The theory of survival models is addressed in other texts, including the ACTEX work entitled Models for Quantifying Risk which might be considered a companion text to this one. In Risk Models and Their Estimation we consider as well the estimation of survival models, in both tabular and parametric form, from sample data. This text is a valuable reference for those preparing for Exam C of the Society of Actuaries and Exam 4 of the Casualty Actuarial Society. A separate solutions' manual with detailed solutions to the text exercises is also available.
Download or read book Modern Actuarial Risk Theory written by Rob Kaas and published by Springer Science & Business Media. This book was released on 2008-12-03 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Actuarial Risk Theory contains what every actuary needs to know about non-life insurance mathematics. It starts with the standard material like utility theory, individual and collective model and basic ruin theory. Other topics are risk measures and premium principles, bonus-malus systems, ordering of risks and credibility theory. It also contains some chapters about Generalized Linear Models, applied to rating and IBNR problems. As to the level of the mathematics, the book would fit in a bachelors or masters program in quantitative economics or mathematical statistics. This second and.
Download or read book Collective Risk Assessment in Affordable Care Act Markets written by Juan Ignacio de Oyarbide and published by . This book was released on 2020 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Loss Distributions written by Robert V. Hogg and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to the problem of fitting parametric probability distributions to data, this treatment uniquely unifies loss modeling in one book. Data sets used are related to the insurance industry, but can be applied to other distributions. Emphasis is on the distribution of single losses related to claims made against various types of insurance policies. Includes five sets of insurance data as examples.
Download or read book International Convergence of Capital Measurement and Capital Standards written by and published by Lulu.com. This book was released on 2004 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Systemic Contingent Claims Analysis written by Mr.Andreas A. Jobst and published by International Monetary Fund. This book was released on 2013-02-27 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent global financial crisis has forced a re-examination of risk transmission in the financial sector and how it affects financial stability. Current macroprudential policy and surveillance (MPS) efforts are aimed establishing a regulatory framework that helps mitigate the risk from systemic linkages with a view towards enhancing the resilience of the financial sector. This paper presents a forward-looking framework ("Systemic CCA") to measure systemic solvency risk based on market-implied expected losses of financial institutions with practical applications for the financial sector risk management and the system-wide capital assessment in top-down stress testing. The suggested approach uses advanced contingent claims analysis (CCA) to generate aggregate estimates of the joint default risk of multiple institutions as a conditional tail expectation using multivariate extreme value theory (EVT). In addition, the framework also helps quantify the individual contributions to systemic risk and contingent liabilities of the financial sector during times of stress.
Download or read book Pricing in General Insurance written by Pietro Parodi and published by CRC Press. This book was released on 2014-10-15 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the syllabus of the actuarial industry course on general insurance pricing — with additional material inspired by the author’s own experience as a practitioner and lecturer — Pricing in General Insurance presents pricing as a formalised process that starts with collecting information about a particular policyholder or risk and ends with a commercially informed rate. The main strength of this approach is that it imposes a reasonably linear narrative on the material and allows the reader to see pricing as a story and go back to the big picture at any time, putting things into context. Written with both the student and the practicing actuary in mind, this pragmatic textbook and professional reference: Complements the standard pricing methods with a description of techniques devised for pricing specific products (e.g., non-proportional reinsurance and property insurance) Discusses methods applied in personal lines when there is a large amount of data and policyholders can be charged depending on many rating factors Addresses related topics such as how to measure uncertainty, incorporate external information, model dependency, and optimize the insurance structure Provides case studies, worked-out examples, exercises inspired by past exam questions, and step-by-step methods for dealing concretely with specific situations Pricing in General Insurance delivers a practical introduction to all aspects of general insurance pricing, covering data preparation, frequency analysis, severity analysis, Monte Carlo simulation for the calculation of aggregate losses, burning cost analysis, and more.
