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Author: Yuliya Mishura Publisher: Elsevier ISBN: 0081020988 Category : Mathematics Languages : en Pages : 278
Book Description
Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach deals with continuous-time risk models and covers several aspects of risk theory. The first of them is the smoothness of the survival probabilities. In particular, the book provides a detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities for different risk models. Next, it gives some possible applications of the results concerning the smoothness of the survival probabilities. Additionally, the book introduces the supermartingale approach, which generalizes the martingale one introduced by Gerber, to get upper exponential bounds for the infinite-horizon ruin probabilities in some generalizations of the classical risk model with risky investments. - Provides new original results - Detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities, as well as possible applications of these results - An excellent supplement to current textbooks and monographs in risk theory - Contains a comprehensive list of useful references
Author: Yuliya Mishura Publisher: Elsevier ISBN: 0081020988 Category : Mathematics Languages : en Pages : 278
Book Description
Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach deals with continuous-time risk models and covers several aspects of risk theory. The first of them is the smoothness of the survival probabilities. In particular, the book provides a detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities for different risk models. Next, it gives some possible applications of the results concerning the smoothness of the survival probabilities. Additionally, the book introduces the supermartingale approach, which generalizes the martingale one introduced by Gerber, to get upper exponential bounds for the infinite-horizon ruin probabilities in some generalizations of the classical risk model with risky investments. - Provides new original results - Detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities, as well as possible applications of these results - An excellent supplement to current textbooks and monographs in risk theory - Contains a comprehensive list of useful references
Author: S?ren Asmussen Publisher: World Scientific ISBN: 9814282529 Category : Mathematics Languages : en Pages : 621
Book Description
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.
Author: Soren Asmussen Publisher: World Scientific ISBN: 9814466921 Category : Mathematics Languages : en Pages : 621
Book Description
The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-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.
Author: Gordon E. Willmot Publisher: Springer ISBN: 3319713620 Category : Business & Economics Languages : en Pages : 228
Book Description
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.
Author: Yasutaka Shimizu Publisher: Springer Nature ISBN: 981169284X Category : Business & Economics Languages : en Pages : 119
Book Description
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.
Author: Hanji Shang Publisher: World Scientific ISBN: 9812565051 Category : Mathematics Languages : en Pages : 282
Book Description
Since actuarial education was introduced into China in the 1980s, Chinese scholars have paid greater attention to the theoretical research of actuarial science. Professors and industry experts from well-known universities in China recently worked together on the project ?Insurance Information Processing and Actuarial Mathematics Theory and Methodology?, which was supported by the Chinese government. Summarizing what they achieved, this volume provides a study of some basic problems of actuarial science, including risk models, risk evaluation and analysis, and premium principles. The contributions cover some new applications of probability and statistics, fuzzy mathematics and financial economics to the field of actuarial practices. Discussions on the new insurance market in China are also presented.
Author: Rob Kaas Publisher: Springer Science & Business Media ISBN: 3540867368 Category : Business & Economics Languages : en Pages : 394
Book Description
Modern Actuarial Risk Theory contains what every actuary needs to know about non-life insurance mathematics. It starts with the standard material like utility theory, individual and collective model and basic ruin theory. Other topics are risk measures and premium principles, bonus-malus systems, ordering of risks and credibility theory. It also contains some chapters about Generalized Linear Models, applied to rating and IBNR problems. As to the level of the mathematics, the book would fit in a bachelors or masters program in quantitative economics or mathematical statistics. This second and.
Author: Ricardas Zitikis Publisher: MDPI ISBN: 3039285165 Category : Business & Economics Languages : en Pages : 210
Book Description
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.
Author: Soren Asmussen Publisher: World Scientific ISBN: 9814500321 Category : Mathematics Languages : en Pages : 399
Book Description
The book is a comprehensive treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (eg. 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 or periodicity. Special features of the book are the emphasis on change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas like queueing theory.
Author: Yuliya Mishura
Author: Yuliya Mishura
Author: S?ren Asmussen
Author: Soren Asmussen
Author: Gordon E. Willmot
Author: Yasutaka Shimizu
Author: Hanji Shang
Author: Rob Kaas
Author: Ricardas Zitikis
Author: Soren Asmussen
Author: Roger J. Gray