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Gerber Shiu Risk Theory
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Book Synopsis Gerber–Shiu Risk Theory by : Andreas E. Kyprianou
Download or read book Gerber–Shiu Risk Theory written by Andreas E. Kyprianou and published by Springer Science & Business Media. This book was released on 2013-10-02 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by the many and long-standing contributions of H. Gerber and E. Shiu, this book gives a modern perspective on the problem of ruin for the classical Cramér–Lundberg model and the surplus of an insurance company. The book studies martingales and path decompositions, which are the main tools used in analysing the distribution of the time of ruin, the wealth prior to ruin and the deficit at ruin. Recent developments in exotic ruin theory are also considered. In particular, by making dividend or tax payments out of the surplus process, the effect on ruin is explored. Gerber-Shiu Risk Theory can be used as lecture notes and is suitable for a graduate course. Each chapter corresponds to approximately two hours of lectures.
Book Synopsis Gerber–Shiu Risk Theory by : Andreas Kyprianou
Download or read book Gerber–Shiu Risk Theory written by Andreas Kyprianou and published by Springer. This book was released on 2013-11-27 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by the many and long-standing contributions of H. Gerber and E. Shiu, this book gives a modern perspective on the problem of ruin for the classical Cramér–Lundberg model and the surplus of an insurance company. The book studies martingales and path decompositions, which are the main tools used in analysing the distribution of the time of ruin, the wealth prior to ruin and the deficit at ruin. Recent developments in exotic ruin theory are also considered. In particular, by making dividend or tax payments out of the surplus process, the effect on ruin is explored. Gerber-Shiu Risk Theory can be used as lecture notes and is suitable for a graduate course. Each chapter corresponds to approximately two hours of lectures.
Book Synopsis Gerber-Shiu Theory for Discrete Risk Processes in a Regime Switching Environment by : Zbigniew Palmowski
Download or read book Gerber-Shiu Theory for Discrete Risk Processes in a Regime Switching Environment written by Zbigniew Palmowski and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we develop the Gerber-Shiu theory for the classic and dual discrete risk processes in a Markovian (regime switching) environment. In particular, by expressing the Gerber-Shiu function in terms of potential measures of an upward (downward) skip-free discrete-time and discrete-space Markov Additive Process (MAP), we derive closed form expressions for the Gerber-Shiu function in terms of the so-called (discrete) $ mathbf{W}_{v}$ and $ mathbf{Z}_{v}$ scale matrices, which were introduced in Palmowski et al. (2020). We show that the discrete scale matrices allow for a unified approach for identifying the Gerber-Shiu function as well as the value function of the associated constant dividend barrier problems.
Book Synopsis Asymptotic Statistics in Insurance Risk Theory by : Yasutaka Shimizu
Download or read book Asymptotic Statistics in Insurance Risk Theory written by Yasutaka Shimizu and published by Springer Nature. This book was released on 2022-01-21 with total page 119 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.
Book Synopsis Essentials of Risk Theory by : Sabine Roeser
Download or read book Essentials of Risk Theory written by Sabine Roeser and published by Springer Science & Business Media. This book was released on 2012-11-02 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk has become one of the main topics in fields as diverse as engineering, medicine and economics, and it is also studied by social scientists, psychologists and legal scholars. This Springer Essentials version offers an overview of the in-depth handbook and highlights some of the main points covered in the Handbook of Risk Theory. The topic of risk also leads to more fundamental questions such as: What is risk? What can decision theory contribute to the analysis of risk? What does the human perception of risk mean for society? How should we judge whether a risk is morally acceptable or not? Over the last couple of decades questions like these have attracted interest from philosophers and other scholars into risk theory. This brief offers the essentials of the handbook provides for an overview into key topics in a major new field of research and addresses a wide range of topics, ranging from decision theory, risk perception to ethics and social implications of risk. It aims to promote communication and information among all those who are interested in theoretical issues concerning risk and uncertainty. The Essentials of Risk Theory brings together internationally leading philosophers and scholars from other disciplines who work on risk theory. The contributions are accessibly written and highly relevant to issues that are studied by risk scholars. The Essentials of Risk Theory will be a helpful starting point for all risk scholars who are interested in broadening and deepening their current perspectives.
Book Synopsis Handbook of Risk Theory by : Sabine Roeser
Download or read book Handbook of Risk Theory written by Sabine Roeser and published by Springer Science & Business Media. This book was released on 2012 with total page 1209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk has become one of the main topics in fields as diverse as engineering, medicine and economics, and it is also studied by social scientists, psychologists and legal scholars. But the topic of risk also leads to more fundamental questions such as: What is risk? What can decision theory contribute to the analysis of risk? What does the human perception of risk mean for society? How should we judge whether a risk is morally acceptable or not? Over the last couple of decades questions like these have attracted interest from philosophers and other scholars into risk theory. This handbook provides for an overview into key topics in a major new field of research. It addresses a wide range of topics, ranging from decision theory, risk perception to ethics and social implications of risk, and it also addresses specific case studies. It aims to promote communication and information among all those who are interested in theoetical issues concerning risk and uncertainty. This handbook brings together internationally leading philosophers and scholars from other disciplines who work on risk theory. The contributions are accessibly written and highly relevant to issues that are studied by risk scholars. We hope that the Handbook of Risk Theory will be a helpful starting point for all risk scholars who are interested in broadening and deepening their current perspectives.
Book Synopsis Risk Theory: A Heavy Tail Approach by : Dimitrios George Konstantinides
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 Theory written by E. Beard and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: whioh the developments are appropriate in an elementary text book is open to doubt. Fortunately the proceedings of the conference arranged by the Society of Actuaries Research Committee in September 1974 provide an effective review of the ourrent position (Credibility, Theory and Applications, Ed. P. M. Kahn, Academic Press, 1975). It is doubtful if any practical use is now made of the Esscher approximation and the N-P method is much more convenient and of adequate accuracy in most practical work. Thus the first half of Chapter 6 is now largely of historical interest. Chapter 11 dealing with ruin probability during a finite time interval does not give an adequate view of the current importanoe of this topic but the position is fluid because of the considerable effort being expended in the search for practical methods of calcu lation. Formulae are, in general, complicated and involve extensive computer based quadratures or simulation techniques. The paper by Seal in the Scandinavian Actuarial Journal (The Numerical Calculation of U(w,t) the Probability of Non-ruin in an Interval (O,t) 1974) gives a recent treatment and a fairly complete list of relevant references. In many countries studies are currently in progress in the develop ment of models for business planning where the basic operations involve a stochastic process. Not only are insurance companies interested but in many commercial and industrial firms the needs are significant so that a very large field exists for applications.
Book Synopsis Gerber-Shiu Analysis in Some Dependent Sparre Andersen Risk Models by : Jae-Kyung Woo
Download or read book Gerber-Shiu Analysis in Some Dependent Sparre Andersen Risk Models written by Jae-Kyung Woo and published by . This book was released on 2010 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we consider a generalization of the classical Gerber-Shiu function in various risk models.
Book Synopsis Aspects of Risk Theory by : Jan Grandell
Download or read book Aspects of Risk Theory written by Jan Grandell and published by . This book was released on 1990-12-20 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analysis of Some Risk Models Involving Dependence by : Eric C. K. Cheung
Download or read book Analysis of Some Risk Models Involving Dependence written by Eric C. K. Cheung and published by . This book was released on 2010 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seminal paper by Gerber and Shiu (1998) gave a huge boost to the study of risk theory by not only unifying but also generalizing the treatment and the analysis of various risk-related quantities in one single mathematical function - the Gerber-Shiu expected discounted penalty function, or Gerber-Shiu function in short. The Gerber-Shiu function is known to possess many nice properties, at least in the case of the classical compound Poisson risk model. For example, upon the introduction of a dividend barrier strategy, it was shown by Lin et al. (2003) and Gerber et al. (2006) that the Gerber-Shiu function with a barrier can be expressed in terms of the Gerber-Shiu function without a barrier and the expected value of discounted dividend payments. This result is the so-called dividends-penalty identity, and it holds true when the surplus process belongs to a class of Markov processes which are skip-free upwards. However, one stringent assumption of the model considered by the above authors is that all the interclaim times and the claim sizes are independent, which is in general not true in reality. In this thesis, we propose to analyze the Gerber-Shiu functions under various dependent structures. The main focus of the thesis is the risk model where claims follow a Markovian arrival process (MAP) (see, e.g., Latouche and Ramaswami (1999) and Neuts (1979, 1989)) in which the interclaim times and the claim sizes form a chain of dependent variables. The first part of the thesis puts emphasis on certain dividend strategies. In Chapter 2, it is shown that a matrix form of the dividends-penalty identity holds true in a MAP risk model perturbed by diffusion with the use of integro-differential equations and their solutions. Chapter 3 considers the dual MAP risk model which is a reflection of the ordinary MAP model. A threshold dividend strategy is applied to the model and various risk-related quantities are studied. Our methodology is based on an existing connection between the MAP risk model and a fluid queue (see, e.g., Asmussen et al. (2002), Badescu et al. (2005), Ramaswami (2006) and references therein). The use of fluid flow techniques to analyze risk processes opens the door for further research as to what types of risk model with dependency structure can be studied via probabilistic arguments. In Chapter 4, we propose to analyze the Gerber-Shiu function and some discounted joint densities in a risk model where each pair of the interclaim time and the resulting claim size is assumed to follow a bivariate phase-type distribution, with the pairs assumed to be independent and identically distributed (i.i.d.). To this end, a novel fluid flow process is constructed to ease the analysis. In the classical Gerber-Shiu function introduced by Gerber and Shiu (1998), the random variables incorporated into the analysis include the time of ruin, the surplus prior to ruin and the deficit at ruin. The later part of this thesis focuses on generalizing the classical Gerber-Shiu function by incorporating more random variables into the so-called penalty function. These include the surplus level immediately after the second last claim before ruin, the minimum surplus level before ruin and the maximum surplus level before ruin. In Chapter 5, the focus will be on the study of the generalized Gerber-Shiu function involving the first two new random variables in the context of a semi-Markovian risk model (see, e.g., Albrecher and Boxma (2005) and Janssen and Reinhard (1985)). It is shown that the generalized Gerber-Shiu function satisfies a matrix defective renewal equation, and some discounted joint densities involving the new variables are derived. Chapter 6 revisits the MAP risk model in which the generalized Gerber-Shiu function involving the maximum surplus before ruin is examined. In this case, the Gerber-Shiu function no longer satisfies a defective renewal equation. Instead, the generalized Gerber-Shiu function can be expressed in terms of the classical Gerber-Shiu function and the Laplace transform of a first passage time that are both readily obtainable. In a MAP risk model, the interclaim time distribution must be phase-type distributed. This leads us to propose a generalization of the MAP risk model by allowing for the interclaim time to have an arbitrary distribution. This is the subject matter of Chapter 7. Chapter 8 is concerned with the generalized Sparre Andersen risk model with surplus-dependent premium rate, and some ordering properties of certain ruin-related quantities are studied. Chapter 9 ends the thesis by some concluding remarks and directions for future research.
Download or read book Risk Theory written by Nicholas Rescher and published by Springer Nature. This book was released on 2021-10-04 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Apart from its foray into technical issues of risk assessment and management, this book has one principal aim. With situations of chancy outcomes certain key factors—including outcome possibilities, overall expectation, threat, and even luck—are measurable parameters. But risk is something different: it is not measurable a single parametric quantity, but a many-sided factor that has several different components, and constitutes a complex phenomenon that must be assessed judgmentally in a highly contextualized way. This book explains and analyzes how this works out in practice. Topics in this work include choice and risk, chance and likelihood, as well as outcome-yield evaluation and risk. It takes into account abnormal situations and eccentric measurements, situational evaluation and expectation and scrutinizes the social aspect of risk. The book is of interest to logicians, philosophers of mathematics, and researchers of risk assessment. The project is a companion piece to the author's LUCK THEORY, also published by Springer.
Book Synopsis Insurance Risk and Ruin by : David C. M. Dickson
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.
Book Synopsis Risk Theory Made Easy by : Suzanne Dopyera Kuntz
Download or read book Risk Theory Made Easy written by Suzanne Dopyera Kuntz and published by . This book was released on 1997 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Dimitrios George Konstantinides Publisher :World Scientific Publishing Company ISBN 13 :9789813223141 Total Pages :494 pages Book Rating :4.2/5 (231 download)
Book Synopsis Risk Theory by : Dimitrios George Konstantinides
Download or read book Risk Theory written by Dimitrios George Konstantinides and published by World Scientific Publishing Company. This book was released on 2017-07-10 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface -- Classical risk model -- Renewal risk model -- Ruin probability estimation -- Extreme value theory -- Regular variation -- Ruin under subexponentiality -- Random sums -- The single big jump -- Ruin under constant interest force -- Absolute ruin -- Discrete dependence model -- Ruin under dependence -- Multivariate regular variation -- Bibliography -- Index
Book Synopsis Lectures on Risk Theory by : Klaus D Schmidt
Download or read book Lectures on Risk Theory written by Klaus D Schmidt and published by . This book was released on 1996-01-01 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Risk Theory written by John C. Wooddy and published by . This book was released on 1968 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
