On Discrete-Time Risk Models with Dependence Based on Integer-Valued Time Series Processes
Title | On Discrete-Time Risk Models with Dependence Based on Integer-Valued Time Series Processes PDF eBook |
Author | Jiahui Li |
Publisher | Open Dissertation Press |
Pages | |
Release | 2017-01-26 |
Genre | |
ISBN | 9781361301722 |
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
On Discrete-time Risk Models with Dependence Based on Integer-valued Time Series Processes
Title | On Discrete-time Risk Models with Dependence Based on Integer-valued Time Series Processes PDF eBook |
Author | 黎嘉慧 |
Publisher | |
Pages | 206 |
Release | 2012 |
Genre | Risk (Insurance) |
ISBN |
On Discrete-time Risk Models with Dependence Based on Integer-valued Time Series Processes
Title | On Discrete-time Risk Models with Dependence Based on Integer-valued Time Series Processes PDF eBook |
Author | Jiahui Li (M. Phil.) |
Publisher | |
Pages | 206 |
Release | 2012 |
Genre | Risk (Insurance) |
ISBN |
Handbook of Discrete-Valued Time Series
Title | Handbook of Discrete-Valued Time Series PDF eBook |
Author | Richard A. Davis |
Publisher | CRC Press |
Pages | 484 |
Release | 2016-01-06 |
Genre | Mathematics |
ISBN | 1466577746 |
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
Copula-Based Markov Models for Time Series
Title | Copula-Based Markov Models for Time Series PDF eBook |
Author | Li-Hsien Sun |
Publisher | Springer Nature |
Pages | 141 |
Release | 2020-07-01 |
Genre | Business & Economics |
ISBN | 9811549982 |
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.
Stochastic Models, Statistics and Their Applications
Title | Stochastic Models, Statistics and Their Applications PDF eBook |
Author | Ansgar Steland |
Publisher | Springer Nature |
Pages | 450 |
Release | 2019-10-15 |
Genre | Mathematics |
ISBN | 3030286657 |
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.
Ruin Probabilities
Title | Ruin Probabilities PDF eBook |
Author | S?ren Asmussen |
Publisher | World Scientific |
Pages | 621 |
Release | 2010 |
Genre | Mathematics |
ISBN | 9814282529 |
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.