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Distortion Risk Measures And Multivariate Distributions Based On Skew Normal Settings
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Book Synopsis Distortion Risk Measures and Multivariate Distributions Based on Skew Normal Settings by : Weizhong Tian (Ph. D.)
Download or read book Distortion Risk Measures and Multivariate Distributions Based on Skew Normal Settings written by Weizhong Tian (Ph. D.) and published by . This book was released on 2016 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is divided into two parts: (I) Distortion Risk Measures Based on Skew Normal Settings. The coherent of the new skew normal distortion risk measure and its transform satisfies the classic Capital Asset Pricing Model (CAPM) were obtained, also, some of the properties of the transform for stock price model under logskewnormal are studied, a simulation based on the skew normal transform is given for an insurance payoff function. In addition, properties of flexible skew-generalized t-distributions with normal kernel and cauchy kernal with their corresponding risk measures are studied. Extended versions of Wang transform using two different forms of flexible skew-generalized distribution functions and two different forms of flexible skew-generalized t-distributions were proposed, moreover, the main results that flexible skew-generalized risk measures are both coherent and degree-two tail-preserving for usual bi-atomic risk distributions are obtained. (II) Families of Multivariate Skew Normal Distributions. The class of multivariate extended skew normal distributions is introduced. The properties of this class of distributions, such as, the moment generating function (MGF), probablitity density function, and independence are discussed. Based on this class of distributions, the extended noncentral skew chi-square distribution is defined and its properties are investigated. Also the necessary and sufficient conditions, under which a quadratic form of the model has an extended noncentral skew chi-square distribution, are obtained. For illustration of our main results, several examples are given. The class of multivariate skew slash distributions under different types of setting is introduced and its density function is discussed. A procedure to obtain the Maximum Likelihood estimators for this family is studied. In addition, the Maximum Likelihood estimators for the mixture model based on this family are discussed. For illustration of our main results, an application is studied to show the performance of the proposed algorithm.
Book Synopsis Econometrics of Risk by : Van-Nam Huynh
Download or read book Econometrics of Risk written by Van-Nam Huynh and published by Springer. This book was released on 2014-12-15 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited book contains several state-of-the-art papers devoted to econometrics of risk. Some papers provide theoretical analysis of the corresponding mathematical, statistical, computational, and economical models. Other papers describe applications of the novel risk-related econometric techniques to real-life economic situations. The book presents new methods developed just recently, in particular, methods using non-Gaussian heavy-tailed distributions, methods using non-Gaussian copulas to properly take into account dependence between different quantities, methods taking into account imprecise ("fuzzy") expert knowledge, and many other innovative techniques. This versatile volume helps practitioners to learn how to apply new techniques of econometrics of risk, and researchers to further improve the existing models and to come up with new ideas on how to best take into account economic risks.
Book Synopsis Behavioral Predictive Modeling in Economics by : Songsak Sriboonchitta
Download or read book Behavioral Predictive Modeling in Economics written by Songsak Sriboonchitta and published by Springer Nature. This book was released on 2020-08-05 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents both methodological papers on and examples of applying behavioral predictive models to specific economic problems, with a focus on how to take into account people's behavior when making economic predictions. This is an important issue, since traditional economic models assumed that people make wise economic decisions based on a detailed rational analysis of all the relevant aspects. However, in reality – as Nobel Prize-winning research has shown – people have a limited ability to process information and, as a result, their decisions are not always optimal. Discussing the need for prediction-oriented statistical techniques, since many statistical methods currently used in economics focus more on model fitting and do not always lead to good predictions, the book is a valuable resource for researchers and students interested in the latest results and challenges and for practitioners wanting to learn how to use state-of-the-art techniques.
Book Synopsis Stress Testing and Systemic Risk Measures Using Multivariate Conditional Probability by : Tomaso Aste
Download or read book Stress Testing and Systemic Risk Measures Using Multivariate Conditional Probability written by Tomaso Aste and published by . This book was released on 2020 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: The multivariate conditional probability distribution models the effects of a set of variables onto the statistical properties of another set of variables. In the study of systemic risk in a financial system, the multivariate conditional probability distribution can be used for stress-testing by quantifying the propagation of losses from a set of `stressing' variables to another set of `stressed' variables. In this paper I describe how to compute such conditional probability distributions for the vast family of multivariate elliptical distributions, and in particular for the multivariate Student-t and the multivariate Normal distributions. Measures of stress impact and systemic risk are proposed. An application to the US equity market illustrates the potentials of this approach.
Book Synopsis Random Distortion Risk Measures by : Xin Zang
Download or read book Random Distortion Risk Measures written by Xin Zang and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a random risk measure, named as the random distortionrisk measure. The random distortion risk measure is a generalization of thetraditional deterministic distortion risk measure by randomizing thedeterministic distortion function and the risk distribution respectively,where a stochastic distortion is introduced to randomize the distortionfunction, and a sub-$ sigma $-algebra is introduced for illustrating theinfluence of the known information on the risk distribution. Sometheoretical properties of the random distortion risk measure are provided,such as normalization, conditional positive homogeneity, conditionalcomonotonic additivity, monotonicity in stochastic dominance order, andcontinuity from below, and method for specifying the stochastic distortionand the sub-$ sigma $-algebra is provided. Based on some stochastic axioms,the representation theorem of the random distortion risk measure is proved.For considering the randomization of a given deterministic distortion riskmeasure, some families of random distortion risk measures are introducedwith the stochastic distortions constructed from Poisson process, Brownianmotion and Dirichlet process respectively, and numerical analysis is carriedout for showing the influence of the stochastic distortion and the riskdistribution by focusing on the sample mean, variance, skewness, kurtosis,and the tail behavior of the random distortion risk measures.
Book Synopsis Asymptotic Analysis and Bounds of Multivariate Coherent Risk by : Li Zhu
Download or read book Asymptotic Analysis and Bounds of Multivariate Coherent Risk written by Li Zhu and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A central topic in modern financial and insurance mathematics is the search for new methods to estimate extreme risk (or tail risk) for multivariate financial assets. This research targets this fundamental question about tail risk, and analyzes tail risk for multivariate financial portfolios, using tail conditional expectation (TCE) and tail distortion risk.
Book Synopsis Conditional Tail Risk Measures for Skewed Generalised Hyperbolic Family by : Katja Ignatieva
Download or read book Conditional Tail Risk Measures for Skewed Generalised Hyperbolic Family written by Katja Ignatieva and published by . This book was released on 2017 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper deals with the estimation of loss severity distribution arising from the historical data on univariate and multivariate losses. We present an innovative theoretical framework where the closed-form expression for the tail conditional expectation (TCE) is derived for the skewed general hyperbolic (GH) family of distributions. Skewed GH family is especially suitable for right-skewed positive random variables such as insurance losses. It allows to capture the asymmetry in the distribution of losses that tends to have a heavy right tail. As opposed to a widely used Value-at-Risk, TCE is a coherent risk measure, which takes into account the expected loss in the tail of the distribution. Our theoretical TCE results are verified for different distributions from the skewed GH family including its general cases: Student-t, variance gamma, normal inverse gaussian and hyperbolic distributions. GH family and its special cases turn out to provide excellent fit to univariate and multivariate data on Danish fire losses. TCE risk measure computed for the skewed family of GH distributions provides conservative estimators of risk, addressing the main challenge faced by insurance companies on how to reliably quantify the risk arising from the loss distribution. We extend our analysis to the multivariate framework when modelling portfolio of losses, allowing multivariate GH distribution to capture the combination of correlated risks and demonstrate how TCE of the portfolio can be decomposed into individual components, representing individual risk in the aggregate (portfolio) loss.
Book Synopsis Equivalent Distortion Risk Measures on Moment Spaces by : Dries Cornilly
Download or read book Equivalent Distortion Risk Measures on Moment Spaces written by Dries Cornilly and published by . This book was released on 2018 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: We show that maximizing distortion risk measures over the set of distribution functions with given mean is equivalent to maximizing their concave counterpart. In the case of Value-at-Risk and Tail Value-at-Risk the equivalence also holds when adding information on higher moments.
Book Synopsis Symmetric Multivariate and Related Distributions by : Kai Wang Fang
Download or read book Symmetric Multivariate and Related Distributions written by Kai Wang Fang and published by CRC Press. This book was released on 2018-01-18 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the by now classical Johnson and Kotz Continuous Multivariate Distributions (Wiley, 1972) there have been substantial developments in multivariate distribution theory especially in the area of non-normal symmetric multivariate distributions. The book by Fang, Kotz and Ng summarizes these developments in a manner which is accessible to a reader with only limited background (advanced real-analysis calculus, linear algebra and elementary matrix calculus). Many of the results in this field are due to Kai-Tai Fang and his associates and appeared in Chinese publications only. A thorough literature search was conducted and the book represents the latest work - as of 1988 - in this rapidly developing field of multivariate distributions. The authors are experts in statistical distribution theory.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1804 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Data Depth written by Regina Y. Liu and published by American Mathematical Soc.. This book was released on 2006 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of some of the research presented at the workshop of the same name held in May 2003 at Rutgers University. The workshop brought together researchers from two different communities: statisticians and specialists in computational geometry. The main idea unifying these two research areas turned out to be the notion of data depth, which is an important notion both in statistics and in the study of efficiency of algorithms used in computational geometry. Many of the articles in the book lay down the foundations for further collaboration and interdisciplinary research. Information for our distributors: Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).
Book Synopsis Statistical Methods in Water Resources by : D.R. Helsel
Download or read book Statistical Methods in Water Resources written by D.R. Helsel and published by Elsevier. This book was released on 1993-03-03 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data on water quality and other environmental issues are being collected at an ever-increasing rate. In the past, however, the techniques used by scientists to interpret this data have not progressed as quickly. This is a book of modern statistical methods for analysis of practical problems in water quality and water resources. The last fifteen years have seen major advances in the fields of exploratory data analysis (EDA) and robust statistical methods. The 'real-life' characteristics of environmental data tend to drive analysis towards the use of these methods. These advances are presented in a practical and relevant format. Alternate methods are compared, highlighting the strengths and weaknesses of each as applied to environmental data. Techniques for trend analysis and dealing with water below the detection limit are topics covered, which are of great interest to consultants in water-quality and hydrology, scientists in state, provincial and federal water resources, and geological survey agencies. The practising water resources scientist will find the worked examples using actual field data from case studies of environmental problems, of real value. Exercises at the end of each chapter enable the mechanics of the methodological process to be fully understood, with data sets included on diskette for easy use. The result is a book that is both up-to-date and immediately relevant to ongoing work in the environmental and water sciences.
Book Synopsis Backtesting Value at Risk and Expected Shortfall by : Simona Roccioletti
Download or read book Backtesting Value at Risk and Expected Shortfall written by Simona Roccioletti and published by Springer Gabler. This book was released on 2015-12-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book Simona Roccioletti reviews several valuable studies about risk measures and their properties; in particular she studies the new (and heavily discussed) property of "Elicitability" of a risk measure. More important, she investigates the issue related to the backtesting of Expected Shortfall. The main contribution of the work is the application of "Test 1" and "Test 2" developed by Acerbi and Szekely (2014) on different models and for five global market indexes.
Book Synopsis Measuring Market Risk by : Kevin Dowd
Download or read book Measuring Market Risk written by Kevin Dowd and published by John Wiley & Sons. This book was released on 2003-02-28 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most up-to-date resource on market risk methodologies Financial professionals in both the front and back office require an understanding of market risk and how to manage it. Measuring Market Risk provides this understanding with an overview of the most recent innovations in Value at Risk (VaR) and Expected Tail Loss (ETL) estimation. This book is filled with clear and accessible explanations of complex issues that arise in risk measuring-from parametric versus nonparametric estimation to incre-mental and component risks. Measuring Market Risk also includes accompanying software written in Matlab—allowing the reader to simulate and run the examples in the book.
Book Synopsis Uncertainty Analysis in Econometrics with Applications by : Van-Nam Huynh
Download or read book Uncertainty Analysis in Econometrics with Applications written by Van-Nam Huynh and published by Springer Science & Business Media. This book was released on 2012-12-14 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike uncertain dynamical systems in physical sciences where models for prediction are somewhat given to us by physical laws, uncertain dynamical systems in economics need statistical models. In this context, modeling and optimization surface as basic ingredients for fruitful applications. This volume concentrates on the current methodology of copulas and maximum entropy optimization. This volume contains main research presentations at the Sixth International Conference of the Thailand Econometrics Society held at the Faculty of Economics, Chiang Mai University, Thailand, during January 10-11, 2013. It consists of keynote addresses, theoretical and applied contributions. These contributions to Econometrics are somewhat centered around the theme of Copulas and Maximum Entropy Econometrics. The method of copulas is applied to a variety of economic problems where multivariate model building and correlation analysis are needed. As for the art of choosing copulas in practical problems, the principle of maximum entropy surfaces as a potential way to do so. The state-of-the-art of Maximum Entropy Econometrics is presented in the first keynote address, while the second keynote address focusses on testing stationarity in economic time series data.
Book Synopsis Illustrating Statistical Procedures: Finding Meaning in Quantitative Data by : Ray W. Cooksey
Download or read book Illustrating Statistical Procedures: Finding Meaning in Quantitative Data written by Ray W. Cooksey and published by Springer Nature. This book was released on 2020-05-14 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book occupies a unique position in the field of statistical analysis in the behavioural and social sciences in that it targets learners who would benefit from learning more conceptually and less computationally about statistical procedures and the software packages that can be used to implement them. This book provides a comprehensive overview of this important research skill domain with an emphasis on visual support for learning and better understanding. The primary focus is on fundamental concepts, procedures and interpretations of statistical analyses within a single broad illustrative research context. The book covers a wide range of descriptive, correlational and inferential statistical procedures as well as more advanced procedures not typically covered in introductory and intermediate statistical texts. It is an ideal reference for postgraduate students as well as for researchers seeking to broaden their conceptual exposure to what is possible in statistical analysis.
Book Synopsis Joint Models for Longitudinal and Time-to-Event Data by : Dimitris Rizopoulos
Download or read book Joint Models for Longitudinal and Time-to-Event Data written by Dimitris Rizopoulos and published by CRC Press. This book was released on 2012-06-22 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of interest, e.g., prostate cancer studies where longitudinal PSA level measurements are collected in conjunction with the time-to-recurrence. Joint Models for Longitudinal and Time-to-Event Data: With Applications in R provides a full treatment of random effects joint models for longitudinal and time-to-event outcomes that can be utilized to analyze such data. The content is primarily explanatory, focusing on applications of joint modeling, but sufficient mathematical details are provided to facilitate understanding of the key features of these models. All illustrations put forward can be implemented in the R programming language via the freely available package JM written by the author. All the R code used in the book is available at: http://jmr.r-forge.r-project.org/
