Download or read book Ruin and Related Quantities in Some Advanced Insurance Risk Models written by Lanpeng Ji and published by . This book was released on 2014 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thèse. HEC. 2014

Download or read book Ruin Related Quantities in Insurance Risk Models written by Jingchao Li and published by . This book was released on 2014 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Time Value of Ruin for Insurance Risk Models written by Shuanming Li and published by . This book was released on 2004 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Adaptive Policies and Drawdown Problems in Insurance Risk Models written by Shu Li and published by . This book was released on 2015 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ruin theory studies an insurer's solvency risk, and to quantify such a risk, a stochastic process is used to model the insurer's surplus process. In fact, research on ruin theory dates back to the pioneer works of Lundberg (1903) and Cramer (1930), where the classical compound Poisson risk model (also known as the Cramer-Lundberg model) was first introduced. The research was later extended to the Sparre Andersen risk model, the Markov arrival risk model, the Levy insurance risk model, and so on. However, in most analysis of the risk models, it is assumed that the premium rate per unit time is constant, which does not always reflect accurately the insurance environment. To better reflect the surplus cash flows of an insurance portfolio, there have been some studies (such as those related to dividend strategies and tax models) which allow the premium rate to take different values over time. Recently, Landriault et al. (2012) proposed the idea of an adaptive premium policy where the premium rate charged is based on the behaviour of the surplus process itself. Motivated by their model, the first part of the thesis focuses on risk models including certain adjustments to the premium rate to reflect the recent claim experience. In Chapter 2, we generalize the Gerber-Shiu analysis of the adaptive premium policy model of Landriault et al. (2012). Chapter 3 proposes an experience-based premium policy under the compound Poisson dynamic, where the premium rate changes are based on the increment between successive random review times. In Chapter 4, we examine a drawdown-based regime-switching Levy insurance model, where the drawdown process is used to model an insurer's level of financial distress over time, and to trigger regime-switching (or premium changes). Similarly to ruin problems which examine the first passage time of the risk process below a threshold level, drawdown problems relate to the first time that a drop in value from a historical peak exceeds a certain level (or equivalently the first passage time of the reflected process above a certain level). As such, drawdowns are fundamentally relevant from the viewpoint of risk management as they are known to be useful to detect, measure and manage extreme risks. They have various applications in many research areas, for instance, mathematical finance, applied probability and statistics. Among the common insurance surplus processes in ruin theory, drawdown episodes have been extensively studied in the class of spectrally negative Levy processes, or more recently, its Markov additive generalization. However, far less attention has been paid to the Sparre Andersen risk model, where the claim arrival process is modelled by a renewal process. The difficulty lies in the fact that such a process does not possess the strong Markov property. Therefore, in the second part of the thesis (Chapter 5), we extend the two-sided exit and drawdown analyses to a renewal risk process. In conclusion, the general focus of this thesis is to derive and analyze ruin-related and drawdown-related quantities in insurance risk models with adaptive policies, and assess their risk management impacts. Chapter 6 ends the thesis by some concluding remarks and directions for future research.

Download or read book Surplus Analysis of Sparre Andersen Insurance Risk Processes written by Gordon E. Willmot and published by Springer. This book was released on 2017-12-21 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This carefully written monograph covers the Sparre Andersen process in an actuarial context using the renewal process as the model for claim counts. A unified reference on Sparre Andersen (renewal risk) processes is included, often missing from existing literature. The authors explore recent results and analyse various risk theoretic quantities associated with the event of ruin, including the time of ruin and the deficit of ruin. Particular attention is given to the explicit identification of defective renewal equation components, which are needed to analyse various risk theoretic quantities and are also relevant in other subject areas of applied probability such as dams and storage processes, as well as queuing theory. Aimed at researchers interested in risk/ruin theory and related areas, this work will also appeal to graduate students in classical and modern risk theory and Gerber-Shiu analysis.

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 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 Asymptotic Statistics in Insurance Risk Theory written by Yasutaka Shimizu and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book begins with the fundamental large sample theory, estimating ruin probability, and ends by dealing with the latest issues of estimating the Gerber-Shiu function. This book is the first to introduce the recent development of statistical methodologies in risk theory (ruin theory) as well as their mathematical validities. Asymptotic theory of parametric and nonparametric inference for the ruin-related quantities is discussed under the setting of not only classical compound Poisson risk processes (Cramér-Lundberg model) but also more general Lévy insurance risk processes. The recent development of risk theory can deal with many kinds of ruin-related quantities: the probability of ruin as well as Gerber-Shiu's discounted penalty function, both of which are useful in insurance risk management and in financial credit risk analysis. In those areas, the common stochastic models are used in the context of the structural approach of companies' default. So far, the probabilistic point of view has been the main concern for academic researchers. However, this book emphasizes the statistical point of view because identifying the risk model is always necessary and is crucial in the final step of practical risk management.

Download or read book Ruin Theory Under a Threshold Insurance Risk Model written by Kwok-Man Kwan 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, "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 On Moments and Related Quantities in Insurance Surplus Analysis written by Wing Yan Lee and published by . This book was released on 2014 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: In risk theory, the time to ruin is one of the central quantities. The Laplace transform, density and moments of the time to ruin have been studied by many authors under different risk model assumptions. The Gerber-Shiu function provides an analytic tool in studying these quantities. The main focus of this thesis is to study the moments involving the time to ruin by using the Gerber-Shiu function as the analytic tool.

Download or read book Insurance Risk and Ruin written by David C. M. Dickson and published by Cambridge University Press. This book was released on 2016-10-27 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book is on the two major areas of risk theory: aggregate claims distributions and ruin theory. For aggregate claims distributions, detailed descriptions are given of recursive techniques that can be used in the individual and collective risk models. For the collective model, the book discusses different classes of counting distribution, and presents recursion schemes for probability functions and moments. For the individual model, the book illustrates the three most commonly applied techniques. Beyond the classical topics in ruin theory, this new edition features an expanded section covering time of ruin problems, Gerber–Shiu functions, and the application of De Vylder approximations. Suitable for a first course in insurance risk theory and extensively classroom tested, the book is accessible to readers with a solid understanding of basic probability. Numerous worked examples are included and each chapter concludes with exercises for which complete solutions are provided.

Download or read book On Some Topics in L vy Insurance Risk Models written by Tsun Yu Jeff Wong and published by . This book was released on 2019 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk management has long been the central focus within actuarial science. There are various risks a typical actuarial company would look into, solvency risk being one of them. This falls under the scope of surplus analysis. Studying of an insurer's ability to maintain an adequate surplus level in order to fulfill its future obligation would be the subject matter, which requires modeling of the underlying surplus process together with de fining appropriate matrices to quantity the risk. Ultimately, it aims at accurately reflecting the solvency status to a line of business, which requires developing realistic models to predict the evolution of the underlying surplus and constructing various ruin quantities depending on the regulations or the risk appetite set internally by the company. While there have been a vast amount of literature devoted to answering these questions in the past decades, a considerable amount of effort is devoted by different scholars in recent years to construct more accurate models to work with, and to develop a spectrum of risk quantities to serve different purposes. In the meantime, more advanced tools are also developed to assist with the analysis involved. With the same spirit, this thesis aims at making contributions in these areas. In Chapter 3, a Parisian ruin time is analyzed under a spectrally negative Lévy model. A hybrid observation scheme is investigated, which allows a more frequent monitoring when the solvency status to a business is observed to be critical. From a practical perspective, such observation scheme provides an extra degree of realism. From a theoretical perspective, it unifies analysis to paths having either bounded or unbounded variations, a core obstacle for analysis under the context of spectrally negative Lévy model. Laplace transform to the concerned ruin time is obtained. Existing results in the literature are also retrieved to demonstrate consistency by taking appropriate limits. In Chapter 4, the toolbox of discrete Poissonian observation is further complemented under a spectrally negative Lévy context. By extending the classical definition of potential measures, which summarizes the law of ruin time and deficit at ruin under continuous observation, to its discrete counterpart, expressions to the Poissonian potential measures are derived. An interesting dual relation is also discovered between a Poissonian potential measure and the corresponding exit measure. This further strengthens the motivation for studying the Poissonian potential measures. To further demonstrate its usefulness, several problems are formulated and analyzed at the end of this chapter. In Chapter 5, motivated from regulatory practices, a more conservative risk matrix is constructed by altering the traditional definition to a Parisian ruin time. As a starting point, analysis is performed using a Cram er-Lundberg model, a special case of spectrally negative Lévy model. The law of ruin time and its de cit at ruin is obtained. An interesting ordering property is also argued to justify why it is a more conservative risk measure to work with. To ensure that the thesis flows smoothly, Chapter 1 and 2 are devoted to the background reading. Literature reviews and existing tools necessary for subsequent derivations are provided at the beginning of each chapters to ensure self-containment. A summary and concluding remarks can be found in Chapter 6.

Download or read book The Cram r Lundberg Model and Its Variants written by Michel Mandjes and published by Springer Nature. This book was released on 2023-12-29 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive examination of the Cramér–Lundberg model, which is the most extensively researched model in ruin theory. It covers the fundamental dynamics of an insurance company's surplus level in great detail, presenting a thorough analysis of the ruin probability and related measures for both the standard model and its variants. Providing a systematic and self-contained approach to evaluate the crucial quantities found in the Cramér–Lundberg model, the book makes use of connections with related queueing models when appropriate, and its emphasis on clean transform-based techniques sets it apart from other works. In addition to consolidating a wealth of existing results, the book also derives several new outcomes using the same methodology. This material is complemented by a thoughtfully chosen collection of exercises. The book's primary target audience is master's and starting PhD students in applied mathematics, operations research, and actuarial science, although it also serves as a useful methodological resource for more advanced researchers. The material is self-contained, requiring only a basic grounding in probability theory and some knowledge of transform techniques.

Download or read book Ruin Probabilities and Related Quantities in the Renewal Risk Model with Dependence and Time Delay in Claims Settlement written by Kokou Essiomle and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Analysis of Some Risk Processes in Ruin Theory written by Luyin Liu and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Analysis of Some Risk Processes in Ruin Theory" by Luyin, Liu, 劉綠茵, 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 literature of ruin theory, there have been extensive studies trying to generalize the classical insurance risk model. In this thesis, we look into two particular risk processes considering multi-dimensional risk and dependent structures respectively. The first one is a bivariate risk process with a dividend barrier, which concerns a two-dimensional risk model under a barrier strategy. Copula is used to represent the dependence between two business lines when a common shock strikes. By defining the time of ruin to be the first time that either of the two lines has its surplus level below zero, we derive a discrete approximation procedure to calculate the expected discounted dividends until ruin under such a model. A thorough discussion of application in proportional reinsurance with numerical examples is provided as well as an examination of the joint optimal dividend barrier for the bivariate process. The second risk process is a semi-Markovian dual risk process. Assuming that the dependence among innovations and waiting times is driven by a Markov chain, we analyze a quantity resembling the Gerber-Shiu expected discounted penalty function that incorporates random variables defined before and after the time of ruin, such as the minimum surplus level before ruin and the time of the first gain after ruin. General properties of the function are studied, and some exact results are derived upon distributional assumptions on either the inter-arrival times or the gain amounts. Applications in a perpetual insurance and the last inter-arrival time before ruin are given along with some numerical examples. DOI: 10.5353/th_b5153734 Subjects: Risk (Insurance) - Mathematical models

Download or read book Effective Actuarial Methods written by M. J. Goovaerts and published by North Holland. This book was released on 1990 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last two decades actuarial research has developed in a more applied direction. Although the original risk models generally served as convenient and sometimes tractable mathematical examples of general probabilistic and/or statistical theories, nowadays models and techniques are encountered that can be considered to be typically actuarial. Examples include ordering of risks by dangerousness, credibility theory and techniques based on IBNR models. Not only does this book present the underlying mathematics of these subjects, but it also deals with the practical application of the techniques. In order to provide results based on real insurance portfolios, use is made of three software packages, namely SLIC performing stop-loss insurance calculations for individual and collective risk models, CRAC dealing with actuarial applications of credibility theory, and LORE giving IBNR-based estimates for loss reserves. Worked-out examples illustrate the theoretical results. This book is intended for use in preparing university actuarial exams, and contains many exercises with varying levels of complexity. It is valuable as a textbook for students in actuarial sciences during their last year of study. Due to the emphasis on applications and because of the worked-out examples on real portfolio data, it is also useful for practising actuaries to guide them in interpreting their own results.

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 2007 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: