Download or read book On Discrete Time Risk Models with Dependence Based on Integer Valued Time Series Processes written by Jiahui Li and published by Open Dissertation Press. This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "On Discrete-time Risk Models With Dependence Based on Integer-valued Time Series Processes" by Jiahui, Li, 黎嘉慧, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: In the actuarial literature, dependence structures in risk models have been extensively studied. The main theme of this thesis is to investigate some discrete-time risk models with claim numbers modeled by integer-valued time series processes. The first model is a common shock risk model with temporal dependence between the claim numbers in each individual class of business. Specifically the Poisson MA(1) process and Poisson AR(1) process are considered for the temporal dependence. To study the ruin probability, the equations associated with the adjustment coefficients are derived. Comparisons are also made to assess the impact of the dependence structures on the ruin probability. Another model involving both the correlated classes of business and the time series approach is then studied. Thinning dependence structure is adopted to model the dependence among classes of business. The Poisson MA(1) and Poisson AR(1) processes are used to describe the claim-number processes. Adjustment coefficients and ruin probabilities are examined. Finally a discrete-time risk model with the claim number following a Poisson ARCH process is proposed. In this model, the mean of the current claim number depends on the previous observations. Within this framework, the equation for finding the adjustment coefficient is derived. Numerical studies are also carried out to examine the effect of the Poisson ARCH dependence structure on several risk measures including ruin probability, Value at Risk, and conditional tail expectation. DOI: 10.5353/th_b4852187 Subjects: Time-series analysis Risk (Insurance) - Statistical methods
Download or read book On Discrete time Risk Models with Dependence Based on Integer valued Time Series Processes written by 黎嘉慧 and published by . This book was released on 2012 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Discrete time Risk Models with Dependence Based on Integer valued Time Series Processes written by Jiahui Li (M. Phil.) and published by . This book was released on 2012 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Discrete Valued Time Series written by Richard A. Davis and published by CRC Press. This book was released on 2016-01-06 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model a Wide Range of Count Time Series Handbook of Discrete-Valued Time Series presents state-of-the-art methods for modeling time series of counts and incorporates frequentist and Bayesian approaches for discrete-valued spatio-temporal data and multivariate data. While the book focuses on time series of counts, some of the techniques discussed ca
Download or read book Stochastic Models Statistics and Their Applications written by Ansgar Steland and published by Springer Nature. This book was released on 2019-10-15 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents selected and peer-reviewed contributions from the 14th Workshop on Stochastic Models, Statistics and Their Applications, held in Dresden, Germany, on March 6-8, 2019. Addressing the needs of theoretical and applied researchers alike, the contributions provide an overview of the latest advances and trends in the areas of mathematical statistics and applied probability, and their applications to high-dimensional statistics, econometrics and time series analysis, statistics for stochastic processes, statistical machine learning, big data and data science, random matrix theory, quality control, change-point analysis and detection, finance, copulas, survival analysis and reliability, sequential experiments, empirical processes, and microsimulations. As the book demonstrates, stochastic models and related statistical procedures and algorithms are essential to more comprehensively understanding and solving present-day problems arising in e.g. the natural sciences, machine learning, data science, engineering, image analysis, genetics, econometrics and finance.
Download or read book Copula Based Markov Models for Time Series written by Li-Hsien Sun and published by Springer Nature. This book was released on 2020-07-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides statistical methodologies for time series data, focusing on copula-based Markov chain models for serially correlated time series. It also includes data examples from economics, engineering, finance, sport and other disciplines to illustrate the methods presented. An accessible textbook for students in the fields of economics, management, mathematics, statistics, and related fields wanting to gain insights into the statistical analysis of time series data using copulas, the book also features stand-alone chapters to appeal to researchers. As the subtitle suggests, the book highlights parametric models based on normal distribution, t-distribution, normal mixture distribution, Poisson distribution, and others. Presenting likelihood-based methods as the main statistical tools for fitting the models, the book details the development of computing techniques to find the maximum likelihood estimator. It also addresses statistical process control, as well as Bayesian and regression methods. Lastly, to help readers analyze their data, it provides computer codes (R codes) for most of the statistical methods.
Download or read book Ruin Probabilities written by S?ren Asmussen and published by World Scientific. This book was released on 2010 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramr?Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber?Shiu functions and dependence.
Download or read book Count Time Series written by Konstantinos Fokianos and published by CRC Press. This book was released on 2020-06-30 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete time Insurance Risk Models with Dependence Structures written by Kam-pui Wat and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modeling Discrete Time to Event Data written by Gerhard Tutz and published by Springer. This book was released on 2016-06-14 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on statistical methods for the analysis of discrete failure times. Failure time analysis is one of the most important fields in statistical research, with applications affecting a wide range of disciplines, in particular, demography, econometrics, epidemiology and clinical research. Although there are a large variety of statistical methods for failure time analysis, many techniques are designed for failure times that are measured on a continuous scale. In empirical studies, however, failure times are often discrete, either because they have been measured in intervals (e.g., quarterly or yearly) or because they have been rounded or grouped. The book covers well-established methods like life-table analysis and discrete hazard regression models, but also introduces state-of-the art techniques for model evaluation, nonparametric estimation and variable selection. Throughout, the methods are illustrated by real life applications, and relationships to survival analysis in continuous time are explained. Each section includes a set of exercises on the respective topics. Various functions and tools for the analysis of discrete survival data are collected in the R package discSurv that accompanies the book.
Download or read book Discrete time Insurance Risk Models with Dependence Structures written by Kam-pui Wat and published by . This book was released on 2012 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Time Risk Models With Random Premiums written by Llewellyn Hillyer Smith and published by . This book was released on 2019 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past century insurance companies relied to a large extent on the continuous time Mathematical Risk Model proposed by Lundberg, known for its ability to estimate the probability of ruin(capital reserve falling below zero), given the initial capital, linear premium rate and cumulative random size claims occurring at random times. In this Dissertation we introduce a discrete time risk model that allows random premiums, and derive the estimates of the ruin probabilities on both finite and infinite time horizons. Tools applied are drawn from modern probability and include,Martingales, Invariance Principle for Brownian motions, and Large Deviation Principle for the asymptotics of rare events. Our considerations can be dubbed "end of the day model", as ruin is neither declared nor acted upon when it falls between successive discrete times.
Download or read book Non Linear Time Series written by Kamil Feridun Turkman and published by Springer. This book was released on 2014-09-29 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a useful combination of probabilistic and statistical tools for analyzing nonlinear time series. Key features of the book include a study of the extremal behavior of nonlinear time series and a comprehensive list of nonlinear models that address different aspects of nonlinearity. Several inferential methods, including quasi likelihood methods, sequential Markov Chain Monte Carlo Methods and particle filters, are also included so as to provide an overall view of the available tools for parameter estimation for nonlinear models. A chapter on integer time series models based on several thinning operations, which brings together all recent advances made in this area, is also included. Readers should have attended a prior course on linear time series, and a good grasp of simulation-based inferential methods is recommended. This book offers a valuable resource for second-year graduate students and researchers in statistics and other scientific areas who need a basic understanding of nonlinear time series.
Download or read book Recent Studies on Risk Analysis and Statistical Modeling written by Teresa A. Oliveira and published by Springer. This book was released on 2018-08-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the latest developments in the field of risk analysis (RA). Statistical methodologies have long-since been employed as crucial decision support tools in RA. Thus, in the context of this new century, characterized by a variety of daily risks - from security to health risks - the importance of exploring theoretical and applied issues connecting RA and statistical modeling (SM) is self-evident. In addition to discussing the latest methodological advances in these areas, the book explores applications in a broad range of settings, such as medicine, biology, insurance, pharmacology and agriculture, while also fostering applications in newly emerging areas. This book is intended for graduate students as well as quantitative researchers in the area of RA.
Download or read book Time Series in Economics and Finance written by Tomas Cipra and published by Springer Nature. This book was released on 2020-08-31 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the principles and methods for the practical analysis and prediction of economic and financial time series. It covers decomposition methods, autocorrelation methods for univariate time series, volatility and duration modeling for financial time series, and multivariate time series methods, such as cointegration and recursive state space modeling. It also includes numerous practical examples to demonstrate the theory using real-world data, as well as exercises at the end of each chapter to aid understanding. This book serves as a reference text for researchers, students and practitioners interested in time series, and can also be used for university courses on econometrics or computational finance.
Download or read book Introduction to Matrix Analytic Methods in Stochastic Modeling written by G. Latouche and published by SIAM. This book was released on 1999-01-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner.
Download or read book Introduction to Time Series and Forecasting written by Peter J. Brockwell and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some of the key mathematical results are stated without proof in order to make the underlying theory acccessible to a wider audience. The book assumes a knowledge only of basic calculus, matrix algebra, and elementary statistics. The emphasis is on methods and the analysis of data sets. The logic and tools of model-building for stationary and non-stationary time series are developed in detail and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills in this area. The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space models, with an optional chapter on spectral analysis. Additional topics include harmonic regression, the Burg and Hannan-Rissanen algorithms, unit roots, regression with ARMA errors, structural models, the EM algorithm, generalized state-space models with applications to time series of count data, exponential smoothing, the Holt-Winters and ARAR forecasting algorithms, transfer function models and intervention analysis. Brief introducitons are also given to cointegration and to non-linear, continuous-time and long-memory models. The time series package included in the back of the book is a slightly modified version of the package ITSM, published separately as ITSM for Windows, by Springer-Verlag, 1994. It does not handle such large data sets as ITSM for Windows, but like the latter, runs on IBM-PC compatible computers under either DOS or Windows (version 3.1 or later). The programs are all menu-driven so that the reader can immediately apply the techniques in the book to time series data, with a minimal investment of time in the computational and algorithmic aspects of the analysis.
