Download or read book Modelling Multivariate Dependence Structures in Insurance and Credit Risk Via Copulas written by Siti Norafidah Mohd Ramli and published by . This book was released on 2014 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This PhD thesis seeks to offer a new framework that accommodates dependency in pricing an insurance portfolio following the renewal risk model, corporate bonds, as well as credit default swaps (CDS). This will be achieved by combining the approach and methodology of actuarial science with stochastic processes and probability theories, as well as employing a hint of the integral calculus used in the electromagnetic and viscoelasticity fields. [...]." -- Abstract.

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 Multiple Risk Factor Dependence Structures written by Jianxi Su and published by . This book was released on 2016 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a class of dependence structures, that we call the Multiple Risk Factor (MRF) dependence structures. On the one hand, the new constructions extend the popular CreditRisk approach, and as such they formally describe default risk portfolios exposed to an arbitrary number of fatal risk factors with conditionally exponential and dependent hitting (or occurrence) times. On the other hand, the MRF structures can be seen as an encompassing family of multivariate probability distributions with univariate margins distributed Pareto of the 2nd kind, and in this role they can be used to model insurance risk portfolios of dependent and heavy tailed risk components.

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 483 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 factor models that extend from the Gaussian assumption to copulas. It also discusses other multivariate constructions and parametric copula families that have different tail properties and presents extensive material on dependence and tail properties to assist in copula model selection. The author shows how numerical methods and algorithms for inference and simulation are important in high-dimensional copula applications. He presents the algorithms as pseudocode, illustrating their implementation for high-dimensional copula models. He also incorporates results to determine dependence and tail properties of multivariate distributions for future constructions of copula models.

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 Contributions to Static and Time varying Copula based Modeling of Multivariate Association written by Martin Ruppert and published by BoD – Books on Demand. This book was released on 2012 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Putting a particular emphasis on nonparametric methods that rely on modern empirical process techniques, the author contributes to the theory of static and time-varying stochastic models for multivariate association based on the concept of copulas. These functions enable a profound understanding of multivariate association, which is pivotal for judging whether a large set of risky assets entails diversification effects or aggravates risk from an entrepreneurial point of view. Since serial dependence is a stylized fact of financial time series, an asymptotic theory for estimating the structure of association in this context is developed under weak assumptions. A new measure of multivariate association, based on a notion of distance to stochastic independence, is introduced. Asymptotic results as well as hypothesis tests are established which are directly applicable to important types of multivariate financial time series. To ensure that risk management properly captures the current structure of association, it is crucial to assess the constancy of the structure. Therefore, nonparametric tests for a constant copula with either a specified or unspecified change point (candidate) are derived. The thesis concludes with a study of characterizations of association between non-continuous random variables.

Download or read book Modeling Dependence Induced by a Common Random Effect and Risk Measures with Insurance Applications written by Junjie Liu and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random effects models are of particular importance in modeling heterogeneity. A commonly used random effects model for multivariate survival analysis is the frailty model. In this thesis, a special frailty model with an Archimedean dependence structure is used to model dependent risks. This modeling approach allows the construction of multivariate distributions through a copula with univariate marginal distributions as parameters. Copulas are constructed by modeling distribution functions and survival functions, respectively. Measures of the dependence are applied for the copula model selections. Tail-based risk measures for the functions of two dependent variables are investigated for particular interest. The statistical application of the copula modeling approach to an insurance data set is discussed where losses and loss adjustment expenses data are used. Insurance applications based on the fitted model are illustrated.

Download or read book An Introduction to Copulas written by Roger B. Nelsen and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.

Download or read book Multivariate GARCH and Dynamic Copula Models for Financial Time Series written by Martin Grziska and published by Pro BUSINESS. This book was released on 2015-02-05 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents several non-parametric and parametric models for estimating dynamic dependence between financial time series and evaluates their ability to precisely estimate risk measures. Furthermore, the different dependence models are used to analyze the integration of emerging markets into the world economy. In order to analyze numerous dependence structures and to discover possible asymmetries, two distinct model classes are investigated: the multivariate GARCH and Copula models. On the theoretical side a new dynamic dependence structure for multivariate Archimedean Copulas is introduced which lifts the prevailing restriction to two dimensions and extends the multivariate dynamic Archimedean Copulas to more than two dimensions. On this basis a new mixture copula is presented using the newly invented multivariate dynamic dependence structure for the Archimedean Copulas and mixing it with multivariate elliptical copulas. Simultaneously a new process for modeling the time-varying weights of the mixture copula is introduced: this specification makes it possible to estimate various dependence structures within a single model. The empirical analysis of different portfolios shows that all equity portfolios and the bond portfolios of the emerging markets exhibit negative asymmetries, i.e. increasing dependence during market downturns. However, the portfolio consisting of the developed market bonds does not show any negative asymmetries. Overall, the analysis of the risk measures reveals that parametric models display portfolio risk more precisely than non-parametric models. However, no single parametric model dominates all other models for all portfolios and risk measures. The investigation of dependence between equity and bond portfolios of developed countries, proprietary, and secondary emerging markets reveals that secondary emerging markets are less integrated into the world economy than proprietary. Thus, secondary emerging markets are moresuitable to diversify a portfolio consisting of developed equity or bond indices than proprietary.

Download or read book Dependence and the Copula Approach written by Xin Chen and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper aims to introduce the essence of dependence in modern finance, especially in the field of insurance and credit modelling, and to study the copulas as a tool to model dependence. In particular, the paper assembles the similarities in the statistical properties in actuarial science and credit modelling, and demonstrates some common copula applications in both of the fields. Also an empirical study is conducted to specifically investigate the sensitivity of default risk associated with the first-to-default (FTD) credit swap with respect to the change of copula dependence structure together with other changing parameters. The results reveal important implications for investment activities, risk modelling, and future dependence modelling with copulas.

Download or read book Handbook of Financial Time Series written by Torben Gustav Andersen and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 1045 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Financial Time Series gives an up-to-date overview of the field and covers all relevant topics both from a statistical and an econometrical point of view. There are many fine contributions, and a preamble by Nobel Prize winner Robert F. Engle.

Download or read book Dependence Modeling written by Harry Joe and published by World Scientific. This book was released on 2011 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction : Dependence modeling / D. Kurowicka -- 2. Multivariate copulae / M. Fischer -- 3. Vines arise / R.M. Cooke, H. Joe and K. Aas -- 4. Sampling count variables with specified Pearson correlation : A comparison between a naive and a C-vine sampling approach / V. Erhardt and C. Czado -- 5. Micro correlations and tail dependence / R.M. Cooke, C. Kousky and H. Joe -- 6. The Copula information criterion and Its implications for the maximum pseudo-likelihood estimator / S. Gronneberg -- 7. Dependence comparisons of vine copulae with four or more variables / H. Joe -- 8. Tail dependence in vine copulae / H. Joe -- 9. Counting vines / O. Morales-Napoles -- 10. Regular vines : Generation algorithm and number of equivalence classes / H. Joe, R.M. Cooke and D. Kurowicka -- 11. Optimal truncation of vines / D. Kurowicka -- 12. Bayesian inference for D-vines : Estimation and model selection / C. Czado and A. Min -- 13. Analysis of Australian electricity loads using joint Bayesian inference of D-vines with autoregressive margins / C. Czado, F. Gartner and A. Min -- 14. Non-parametric Bayesian belief nets versus vines / A. Hanea -- 15. Modeling dependence between financial returns using pair-copula constructions / K. Aas and D. Berg -- 16. Dynamic D-vine model / A. Heinen and A. Valdesogo -- 17. Summary and future directions / D. Kurowicka

Download or read book Economic Time Series written by William R. Bell and published by CRC Press. This book was released on 2018-11-14 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic Time Series: Modeling and Seasonality is a focused resource on analysis of economic time series as pertains to modeling and seasonality, presenting cutting-edge research that would otherwise be scattered throughout diverse peer-reviewed journals. This compilation of 21 chapters showcases the cross-fertilization between the fields of time s

Download or read book Dependence Structures Beyond Copulas written by Joerg Rothenbuehler and published by . This book was released on 2005 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quantitative Analysis of Extreme Risks and Extremal Dependence in Insurance and Finance written by Hengxin Cui and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we aim at a quantitative understanding of extreme risks and extremal depen- dence in insurance and finance. We use regularly varying distribution functions in extreme value theory (EVT) to model extreme risks, and apply various tools in multivariate extreme value theory (MEVT) to capture extremal dependence. We focus on developing asymptotics for certain risk measures. We start with a portfolio diversification problem. In finance, investors usually construct a mixed portfolio in order to diversify away the individual risks. However, this is not always the case when heavy-tailedness and tail dependence of large losses are considered. Chapter 3 applies the multivariate regular variation (MRV) model to study this problem in an asymptotic sense and provides an applicable portfolio optimization strategy. A practical performance test for our strategy is also provided in this Chapter. The mainstream of the literature on the limitation of portfolio diversification follows the assumption that risks have unbounded distribution support, i.e., no cap for potential loss. However, real-world firms usually have limited liability. Then a natural question arises whether the non-diversification effect strictly depends on the tail behaviour of the loss distribution. For risks with bounded support, will similar non-diversification results still exist? We answer this question in Chapter 4 and we argue that diversification is still possible to be inferior as long as the risks are truncated at sufficiently large threshold level. In Chapter 5, we consider the risk of a large credit portfolio of multiple obligors subject to possible default. Contrary to the Gaussian and t copulas that are widely used in practice, we assume a portfolio dependence structure of Archimedean copula type. Under this setting, we derive sharp asymptotics for portfolio credit risk that highlight the impact of extremal dependence among obligors. By utilizing these asymptotic results, we propose two different algorithms that are shown to be asymptotically optimal and can be applied to efficiently estimate portfolio credit risk via Monte Carlo simulation. In order to capture hierarchical dependence structure among the obligors in a large credit portfolio, we also extend our asymptotic analysis to the structure of nested Gumbel copulas and an efficient algorithm of bounded relative error is also developed for this more complex structure. Numerical results are provided at the end of the chapter to illustrate the performance of our algorithms, as well as their respective merits.

Download or read book Modeling International Financial Returns with a Multivariate Regime Switching Copula written by Loran Chollete and published by . This book was released on 2008 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Multivariate Claim Count Model for Applications in Insurance written by Daniela Anna Selch and published by Springer. This book was released on 2018-08-31 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a time-dynamic model for multivariate claim counts in actuarial applications. Inspired by real-world claim arrivals, the model balances interesting stylized facts (such as dependence across the components, over-dispersion and the clustering of claims) with a high level of mathematical tractability (including estimation, sampling and convergence results for large portfolios) and can thus be applied in various contexts (such as risk management and pricing of (re-)insurance contracts). The authors provide a detailed analysis of the proposed probabilistic model, discussing its relation to the existing literature, its statistical properties, different estimation strategies as well as possible applications and extensions. Actuaries and researchers working in risk management and premium pricing will find this book particularly interesting. Graduate-level probability theory, stochastic analysis and statistics are required.