Download or read book Study on Insurance Risk Models with Subexponential Tails and Dependence Structures written by Yiqing Chen and published by Open Dissertation Press. This book was released on 2017-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Study on Insurance Risk Models With Subexponential Tails and Dependence Structures" by Yiqing, Chen, 陳宜清, 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. DOI: 10.5353/th_b4284176 Subjects: Risk (Insurance) - Mathematical models

Download or read book Study on Insurance Risk Models with Subexponential Tails and Dependence Structures written by Yiqing Chen (actuary.) and published by . This book was released on 2009 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Risk Theory A Heavy Tail Approach written by Dimitrios George Konstantinides and published by #N/A. This book was released on 2017-07-07 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Heavy-tailed risk modelling plays a central role in modern risk theory; within this perspective, the book provides an excellent guide concerning problems and solutions in risk theory.'zbMATHThis book is written to help graduate students and young researchers to enter quickly into the subject of Risk Theory. It can also be used by actuaries and financial practitioners for the optimization of their decisions and further by regulatory authorities for the stabilization of the insurance industry. The topic of extreme claims is especially presented as a crucial feature of the modern ruin probability.

Download or read book Risk Models with Dependence and Perturbation written by Zhong Li and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In ruin theory, the surplus process of an insurance company is usually modeled by the classical compound Poisson risk model or its general version, the Sparre-Andersen risk model. Under these models, the claim amounts and the inter-claim times are assumed to be independently distributed, which is not always appropriate in practice. In recent years, risk models relaxing the independence assumption have drawn increasing attention. However, previous research mostly considers the so call dependent Sparre-Andersen risk model under which the pairs of random variables consisting of the inter-claim time and the next claim amount remain independent of each other. In this thesis, we aim to examine the opposite case. Namely, the distribution of the time until the next claim depends on the size of the previous claim amount. Explicit solutions for the Gerber-Shiu function are provided for arbitrary claim sizes and various ruin-related quantities are obtained as special cases. Numerical examples are also presented. The dependent insurance risk process is further generalized to a perturbed version to incorporate small fluctuations of the underlying surplus process. Explicit solutions for the Gerber-Shiu funtion are deduced along with applications and examples. Lastly, we introduce a perturbed dependence structure into the dual risk model and study the ruin time problem. Exact solutions for the Laplace transform and the first moment of the time to ruin with an arbitrary gain-size distribution are obtained. Applications with numerical examples are provided to illustrate the impact of the dependence structure and the perturbation.

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 Ruin Theory Under a Threshold Insurance Risk Model written by Kwok-Man Kwan and published by . This book was released on 2017-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Ruin Theory Under a Threshold Insurance Risk Model" by Kwok-man, Kwan, 關國文, 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: Abstract of the thesis entitled RUIN THEORY UNDER A THRESHOLD INSURANCE RISK MODEL submitted by Kwan, Kwok Man for the degree of Master of Philosophy at The University of Hong Kong in April 2007 Since the classical Lundberg model was studied in 1903, there have been many studies about the generalization of the classical insurance risk model. The most popular ones are the Sparre-Anderson model, the Markov-modulated model and the di(R)usion-perturbed model. Recently, more and more attentions have been paid to the dependent models. The risk models with dependent claim sizes and the common shock models with di(R)erent lines of business have been studied by many authors. This thesis studies two risk models with dependence between claim size and inter-arrivaltimethroughathresholdstructure.Intherstinsuranceriskmodel, the distribution of the inter-arrival time depends on the last claim size: when the lastclaimsizeisbelowathreshold, thecurrentinter-arrivaltimefollowsacertain probability distribution; otherwise, it follows another probability distribution. Inthe second insurance risk model, its dependence relation is the reversal of the previous one, that is: when the last inter-arrival time is below a threshold, the current claim size follows a certain probability distribution; otherwise, it follows another probability distribution. It was found that the ruin probability became a dicult problem when the model involved these dependent structures. In order to obtain the solution of the ultimate ruin probability for these de- pendent models, the integro-di(R)erential equation, the integral equation and the Laplace transform satised by the ruin probability were derived and the explicit formula of the ruin probability was obtained in the case of exponential claim size. DOI: 10.5353/th_b3832003 Subjects: Risk (Insurance) - Mathematical models Probabilities

Download or read book Actuarial Theory for Dependent Risks written by Michel Denuit and published by John Wiley & Sons. This book was released on 2006-05-01 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The increasing complexity of insurance and reinsurance products has seen a growing interest amongst actuaries in the modelling of dependent risks. For efficient risk management, actuaries need to be able to answer fundamental questions such as: Is the correlation structure dangerous? And, if yes, to what extent? Therefore tools to quantify, compare, and model the strength of dependence between different risks are vital. Combining coverage of stochastic order and risk measure theories with the basics of risk management and stochastic dependence, this book provides an essential guide to managing modern financial risk. * Describes how to model risks in incomplete markets, emphasising insurance risks. * Explains how to measure and compare the danger of risks, model their interactions, and measure the strength of their association. * Examines the type of dependence induced by GLM-based credibility models, the bounds on functions of dependent risks, and probabilistic distances between actuarial models. * Detailed presentation of risk measures, stochastic orderings, copula models, dependence concepts and dependence orderings. * Includes numerous exercises allowing a cementing of the concepts by all levels of readers. * Solutions to tasks as well as further examples and exercises can be found on a supporting website. An invaluable reference for both academics and practitioners alike, Actuarial Theory for Dependent Risks will appeal to all those eager to master the up-to-date modelling tools for dependent risks. The inclusion of exercises and practical examples makes the book suitable for advanced courses on risk management in incomplete markets. Traders looking for practical advice on insurance markets will also find much of interest.

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 Modelling Extremal Events written by Paul Embrechts and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A reader's first impression on leafing through this book is of the large number of graphs and diagrams, used to illustrate shapes of distributions...and to show real data examples in various ways. A closer reading reveals a nice mix of theory and applications, with the copious graphical illustrations alluded to. Such a mixture is of course dear to the heart of the applied probabilist/statistician, and should impress even the most ardent theorists." --MATHEMATICAL REVIEWS

Download or read book Risk Ruin and Survival written by Ricardas Zitikis and published by MDPI. This book was released on 2020-04-02 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developing techniques for assessing various risks and calculating probabilities of ruin and survival are exciting topics for mathematically-inclined academics. For practicing actuaries and financial engineers, the resulting insights have provided enormous opportunities but also created serious challenges to overcome, thus facilitating closer cooperation between industries and academic institutions. In this book, several renown researchers with extensive interdisciplinary research experiences share their thoughts that, in one way or another, contribute to the betterment of practice and theory of decision making under uncertainty. Behavioral, cultural, mathematical, and statistical aspects of risk assessment and modelling have been explored, and have been often illustrated using real and simulated data. Topics range from financial and insurance risks to security-type risks, from one-dimensional to multi- and even infinite-dimensional risks. The articles in the book were written with a broad audience in mind and should provide enjoyable reading for those with university level degrees and/or those who have studied for accreditation by various actuarial and financial societies.

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 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 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 RUIN ANALYSIS OF CORRELATED AG written by Lai-Mei Wan and published by Open Dissertation Press. This book was released on 2017-01-27 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Ruin Analysis of Correlated Aggregate Claims Models" by Lai-mei, Wan, 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: Abstract of thesis entitled RUIN ANALYSIS OF CORRELATED AGGREGATE CLAIMS MODELS Submitted by WAN LAI MEI for the degree of Master of Philosophy at The University of Hong Kong in January 2005 In recent years, study of risk models with dependent classes of insurance business has become a popular topic in actuarial science. The main theme of this the- sis is to explore more general models which include various types of dependence structures among classes in a book of insurance business. Specifically, ruin anal- ysis was performed on two correlated aggregate claims models for a book of m (m>= 2) dependent classes of insurance business. Firstly, a discrete-time risk model was considered with m dependent classes of business in which a time-series approach was adopted. The claim processes of the m classes were assumed to follow a multivariate autoregressive time-series model of order 1. In this framework, different classes were dependent due to the time-series structure and the correlation among current claims. The probability of ruin for the risk model was studied. In the case of m = 2, simulation studiesfor absolutely continuous bivariate exponential (ACBVE) claim distribution and bivariate gamma claim distribution were performed. Next, a continuous-time risk model with m dependent classes of insurance business was investigated. The claim-number processes of the m classes were correlated due to the so-called thinning dependence together with a common shock. Various aspects of the proposed model were examined, and the impact of therelationofdependenceviatheadjustmentcoefficientwasthenstudied. Inthe bivariate case (m = 2), a numerical study was performed for exponential claim distribution and simulation studies were carried out for non-exponential claim distributions. DOI: 10.5353/th_b3070570 Subjects: Risk (Insurance) Probabilities Insurance claims - Mathematical models Insurance - Mathematics

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 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.

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.