Download or read book Copula Based Risks Classification Models for General Insurance written by Joseph Kyalo Mung'atu and published by LAP Lambert Academic Publishing. This book was released on 2015-03-06 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: In risk classification, similar risks should be assigned to the same class with respect to each variable to ease their management. The dependencies among the risks are examined by fitting copulas, estimating the dependence parameters and lastly using distance matrices to cluster the risks together. Distances used in the classification were determined by the problem at hand. The empirical study derived its data from the general insurance business in Kenya where the risks were classified by the Copula based approach. The motivation of the study was driven by the fact that insurance companies had collapsed in the past, one reason being the type of business classes they collectively engaged in. It is therefore important to understand the dependencies between risks for better risk management. This work proposed the use of the upper tail dependence, measured by the tail index, derived from the dependence parameter in determining the retention limits for a re-insurance arrangement. This will ensure that the highly dependent risks in the upper tail will forward higher proportion to the re-insurer and vice versa.

Download or read book Copula Based Multivariate Models with Applications to Risk Management and Insurance written by Marco Bee and published by . This book was released on 2005 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper consists in analysing the relevance of dependence concepts in finance, insurance and risk management, exploring how these concepts can be implemented in a statistical model via copula functions and pointing out some difficulties related to this methodology. In particular, we first review the statistical models currently used in the actuarial and financial fields when dealing with loss data; then we show, by means of two risk management applications, that copula-based models are very flexible but sometimes difficult to set up and to estimate; finally we study, by means of a simulation experiment, the properties of the maximum likelihood estimators of the Gaussian and Gumbel copula.

Download or read book Fundamental Aspects of Operational Risk and Insurance Analytics written by Marcelo G. Cruz and published by John Wiley & Sons. This book was released on 2015-01-29 with total page 939 pages. Available in PDF, EPUB and Kindle. Book excerpt: A one-stop guide for the theories, applications, and statistical methodologies essential to operational risk Providing a complete overview of operational risk modeling and relevant insurance analytics, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk offers a systematic approach that covers the wide range of topics in this area. Written by a team of leading experts in the field, the handbook presents detailed coverage of the theories, applications, and models inherent in any discussion of the fundamentals of operational risk, with a primary focus on Basel II/III regulation, modeling dependence, estimation of risk models, and modeling the data elements. Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk begins with coverage on the four data elements used in operational risk framework as well as processing risk taxonomy. The book then goes further in-depth into the key topics in operational risk measurement and insurance, for example diverse methods to estimate frequency and severity models. Finally, the book ends with sections on specific topics, such as scenario analysis; multifactor modeling; and dependence modeling. A unique companion with Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk, the handbook also features: Discussions on internal loss data and key risk indicators, which are both fundamental for developing a risk-sensitive framework Guidelines for how operational risk can be inserted into a firm’s strategic decisions A model for stress tests of operational risk under the United States Comprehensive Capital Analysis and Review (CCAR) program A valuable reference for financial engineers, quantitative analysts, risk managers, and large-scale consultancy groups advising banks on their internal systems, the handbook is also useful for academics teaching postgraduate courses on the methodology of operational risk.

Download or read book Dependence Modeling and Inference for Insurance Risks written by Marie-Pier Côté and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Modeling the dependence between risks is crucial for the computation of the economic capital and the variability of insurance liabilities. It is thus not surprising that copula (regression) models are widely used in actuarial applications. In this thesis, three topics on dependence modeling for insurance risks are considered. The first part of this work explores the probabilistic features of the dependence structures underlying the background risk model (RX, RY), where R is a strictly positive random variable independent of the random vector (X,Y). This broad class of copulas encompasses Archimedean and elliptical copulas, but also new interesting models, some of which yield explicit expressions for the distribution and tail-value-at-risk of the sum RX+RY. The remainder of the thesis is more statistical in nature. There are numerous actuarial applications of copula models where marginal distributions vary with covariates, but few tools are available for inference in that context. In the second part of the thesis, the validity of rank-based tools for copula inference is established under carefully designed assumptions that hold for all the covariate dependent marginal distributions commonly used for modeling insurance data. Simulation studies are performed in two property and casualty insurance examples: loss triangles for two lines of business and micro-level multivariate claim amounts. The latter example is treated in details in a Bayesian data analysis reported in the last part of this thesis. The model accounts for the dependence between claimants involved in a single event and between amounts paid to a claimant under different insurance coverages. A multiple imputation procedure allows to include the information contained in open claimant files, without which the inference is biased towards simple claims." --

Download or read book Copula Based Hierarchical Risk Aggregation Tree Dependent Sampling and the Space of Mild Tree Dependence written by Fabio Derendinger and published by . This book was released on 2015 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ability to adequately model risks is crucial for insurance companies. The method of "Copula-based hierarchical risk aggregation" by Arbenz et al. offers a flexible way in doing so and has attracted much attention recently. We briefly introduce the aggregation tree model as well as the sampling algorithm proposed by they authors.An important characteristic of the model is that the joint distribution of all risk is not fully specified unless an additional assumption (known as "conditional independence assumption") is added. We show that there is numerical evidence that the sampling algorithm yields an approximation of the distribution uniquely specified by the conditional independence assumption. We propose a modified algorithm and provide a proof that under certain conditions the said distribution is indeed approximated by our algorithm.We further determine the space of feasible distributions for a given aggregation tree model in case we drop the conditional independence assumption. We study the impact of the input parameters and the tree structure, which allows conclusions of the way the aggregation tree should be designed.

Download or read book Robust Regression Methods for Insurance Risk Classification written by Esteban Flores and published by LAP Lambert Academic Publishing. This book was released on 2010-10 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk classification is an important actuarial process for Insurance companies. It allows for the underwriting of the best risks, through an appropriate choice of classification variables, and helps set fair premiums in rate-making. Currently, insurance companies mainly use ad-hoc methods for risk classification, more often based on the type of expenses covered than on the distribution of the corresponding losses. The selection of classification variables is also, in general, based on rate-making variables rather than on an optimal choice criteria based on statistical methods. It is known that logistic regression is among the many sophisticated statistical methods used by the banking industry in order to select credit rating variables. Extending the method to insurance risks seems only natural. Insurance risks are not usually classified in only two categories, good and bad, as can be the case in credit rating, but in a larger number of classes. Here we consider the generalization of the model to extend the use of logistic regression to insurance risk classification.

Download or read book Risk Classification by Means of Clustering written by Bernhard Christian Kübler and published by Peter Lang. This book was released on 2010 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Determining risk-adequate insurance premiums is a core issue in actuarial mathematics. This study is specifically concerned with identifying convenient partitions of (general) insurance collectives such that the resulting tariff classes are homogeneous to a maximum extent and - on the other hand - yet large enough to allow for the occurrence of the group balance concept and to end up with reliable estimates of the moments of the claim size distributions. Therefore, the author develops an innovative classification algorithm utilizing a multidimensional cluster approach combined with credibility-theoretical implications. Its construction stems from involving the entire claim information of risks simultaneously and in a suitable manner, and particulary from obtaining optimality regarding the cluster criterions. Under certain conditions, commonly used cross classification schemes are shown to be a particular case of the new approach. Besides desirable theoretical benefits like its generalizing established cross classification systems, an empirical investigation also suggests the practical superiority of the new algorithm.

Download or read book Modeling and Measuring Insurance Risks for a Hierarchical Copula Model Considering IFRS 17 Framework written by Carlos Andrés Araiza Iturria and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, a stochastic approach to insurance risk modeling and measurement that is compliant with the new International Financial Reporting Standards (IFRS 17) is proposed. The compliance is achieved through the use of a semiparametric hierarchical copula which accounts for the dependence between the lines of business of the Canadian auto insurance industry. A model for the marginal unpaid claim liabilities of each line of business based on double generalized linear models is also developed. Development year and accident year effect factors along with an autoregressive feature for residuals enable modeling the dependence between the various entries of the loss triangles in a given line of business. Capital requirements calculations are then performed through simulation; numbers obtained with univariate and multivariate risk measures are compared. Moreover, a risk adjustment for non-financial risk required by IFRS 17 is also computed through a cost of capital approach.

Download or read book Robust Regression Methods for Insurance Risk Classification written by Esteban Flores and published by . This book was released on 2002 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Copula based Techniques for Risk Aggregation Models written by Oriol Roch and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dependent Risk Models with Archimedean Copulas written by Hélène Cossette and published by . This book was released on 2017 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we investigate dependent risk models in which the dependence structure is defined by an Archimedean copula. Using such a structure with specific marginals, we derive explicit expressions for the pdf of the aggregated risk and other related quantities. The common mixture representation of Archimedean copulas is at the basis of a computational strategy proposed to find exact or approximated values of the distribution of the sum of risks in a general setup. Such results are then used to investigate risk models in regard to aggregation, capital allocation and ruin problems. An extension to nested Archimedean copulas is also discussed.

Download or read book Modeling Dependent Risk Process in Insurance with Copula written by Ting Yang and published by . This book was released on 2005 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Copula based Risk Aggregation Modelling written by Marie-Pier Côté and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "A flexible approach is proposed for risk aggregation. The model consists of a tree structure, bivariate copulas, and marginal distributions. The construction relies on a conditional independence assumption whose implications are studied. A procedure for selecting the tree structure is developed using hierarchical clustering techniques, along with a distance metric based on Kendall's tau. Estimation, simulation, and model validation are also discussed. The approach is illustrated using data from a Canadian property and casualty insurance company." --

Download or read book Dependence Modeling with Copulas written by Harry Joe and published by CRC Press. This book was released on 2014-06-26 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dependence Modeling with Copulas covers the substantial advances that have taken place in the field during the last 15 years, including vine copula modeling of high-dimensional data. Vine copula models are constructed from a sequence of bivariate copulas. The book develops generalizations of vine copula models, including common and structured facto

Download or read book Applying risk classification method in car insurance market written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A estimação do risco em seguros de automóveis representa um difícilproblema de regressão. As dificuldades vão desde a utilização de um grandenúmero de variáveis discretas como explicativas, até a distribuição particular dosruídos e uma quantidade expressiva de categorias com valores nulos e valoresdiscrepantes. Supondo que os problemas de estimação estejam relacionados com aclassificação do risco adotada pelo mercado, este trabalho propõe um método declassificação alternativo. O método desenvolvido foi baseado na técnica de análisefatorial, e no algoritmo de agrupamento de dados denominado fuzzy clusteringsystem. Para avaliar a eficiência do método em solucionar os problemas deestimação, optou-se por utilizar o erro resultante da aplicação de modelos linearesgeneralizados. Ao final, o erro de estimação obtido diante da classificaçãoproposta, foi comparado ao obtido diante da classificação usual de mercado.

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 A Comparative Analysis of Alternative Risk Classification Models in Automobile Insurance written by Beom-Ha Jee and published by . This book was released on 1987 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: