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Author: Gordon E. Willmot Publisher: Springer ISBN: 3319713620 Category : Business & Economics Languages : en Pages : 225
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: Gordon E. Willmot Publisher: Springer ISBN: 3319713620 Category : Business & Economics Languages : en Pages : 225
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: Vsevolod K. Malinovskii Publisher: CRC Press ISBN: 1000411079 Category : Mathematics Languages : en Pages : 340
Book Description
Risk Measures and Insurance Solvency Benchmarks: Fixed-Probability Levels in Renewal Risk Models is written for academics and practitioners who are concerned about potential weaknesses of the Solvency II regulatory system. It is also intended for readers who are interested in pure and applied probability, have a taste for classical and asymptotic analysis, and are motivated to delve into rather intensive calculations. The formal prerequisite for this book is a good background in analysis. The desired prerequisite is some degree of probability training, but someone with knowledge of the classical real-variable theory, including asymptotic methods, will also find this book interesting. For those who find the proofs too complicated, it may be reassuring that most results in this book are formulated in rather elementary terms. This book can also be used as reading material for basic courses in risk measures, insurance mathematics, and applied probability. The material of this book was partly used by the author for his courses in several universities in Moscow, Copenhagen University, and in the University of Montreal. Features Requires only minimal mathematical prerequisites in analysis and probability Suitable for researchers and postgraduate students in related fields Could be used as a supplement to courses in risk measures, insurance mathematics and applied probability.
Author: Michel Mandjes Publisher: Springer Nature ISBN: 3031391055 Category : Mathematics Languages : en Pages : 252
Book Description
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.
Author: Remigijus Leipus Publisher: Springer Nature ISBN: 3031345533 Category : Mathematics Languages : en Pages : 99
Book Description
This book provides a compact and systematic overview of closure properties of heavy-tailed and related distributions, including closure under tail equivalence, convolution, finite mixing, maximum, minimum, convolution power and convolution roots, and product-convolution closure. It includes examples and counterexamples that give an insight into the theory and provides numerous references to technical details and proofs for a deeper study of the subject. The book will serve as a useful reference for graduate students, young researchers, and applied scientists.
Author: Publisher: John Wiley & Sons ISBN: 0470035498 Category : Mathematics Languages : en Pages : 2163
Book Description
Leading the way in this field, the Encyclopedia of Quantitative Risk Analysis and Assessment is the first publication to offer a modern, comprehensive and in-depth resource to the huge variety of disciplines involved. A truly international work, its coverage ranges across risk issues pertinent to life scientists, engineers, policy makers, healthcare professionals, the finance industry, the military and practising statisticians. Drawing on the expertise of world-renowned authors and editors in this field this title provides up-to-date material on drug safety, investment theory, public policy applications, transportation safety, public perception of risk, epidemiological risk, national defence and security, critical infrastructure, and program management. This major publication is easily accessible for all those involved in the field of risk assessment and analysis. For ease-of-use it is available in print and online.
Author: Vladimir Panov Publisher: Springer ISBN: 331965313X Category : Mathematics Languages : en Pages : 511
Book Description
This book brings together the latest findings in the area of stochastic analysis and statistics. The individual chapters cover a wide range of topics from limit theorems, Markov processes, nonparametric methods, acturial science, population dynamics, and many others. The volume is dedicated to Valentin Konakov, head of the International Laboratory of Stochastic Analysis and its Applications on the occasion of his 70th birthday. Contributions were prepared by the participants of the international conference of the international conference “Modern problems of stochastic analysis and statistics”, held at the Higher School of Economics in Moscow from May 29 - June 2, 2016. It offers a valuable reference resource for researchers and graduate students interested in modern stochastics.
Author: S. Ramasubramanian Publisher: Springer ISBN: 9386279444 Category : Mathematics Languages : en Pages : 212
Book Description
Insurance has become a necessary aspect of modern society. The mathematical basis of insurance modeling is best expressed in terms of continuous time stochastic processes. This introductory text on actuarial risk theory deals with the Cramer-Lundberg model and the renewal risk model. Their basic structure and properties, including the renewal theorems as well as the corresponding ruin problems, are studied. There is a detailed discussion of heavy tailed distributions, which have become increasingly relevant. The Lundberg risk process with investment in risky asset is also considered. This book will be useful to practitioners in the field and to graduate students interested in this important branch of applied probability.
Author: Xiaozhen Qi Publisher: Open Dissertation Press ISBN: 9781361029749 Category : Mathematics Languages : en Pages : 88
Book Description
This dissertation, "Analysis of the Generalized Gerber-Shiu Function in Discrete-time Dependent Sparre Andersen Model" by Xiaozhen, Qi, 亓孝真, 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: There is a vast literature in the analysis of the insurer's surplus process under the Sparre Andersen risk model. Since it is cumbersome to calculate distributions of ruin-related quantities in the continuous-time model, we shall consider the discrete-time model as a quick approximation to the corresponding ones in the continuous-time model. In this work, we consider the discrete-time setting of the Sparre Andersen risk model and use the generalized Gerber-Shiu function to study various ruin-related quantities associated with variables in the generalized Gerber-Shiu function such as the ladder height and the claim causing ruin. First, the structural properties of the generalized Gerber-Shiu function are obtained and in turn, joint/marginal distributions of ruin-related quantities of our interest are derived. Then we shall assume particular dependency structure for the claim sizes and the interclaim times. In addition to the ordinary risk model, the delayed model has been receiving attention since the occurrence of the last claim before time zero is taken into account to model the process. Hence we shall investigate general results for the Gerber-Shiu function in the delayed model with time-dependent claim and also focus on its relationship with the ordinary model. Finally the Farlie-Gumbel-Mogenstern (FGM) copula is considered to model dependency structure and distributions of the ruin-related quantities such as the claim causing ruin and the last ladder height. We will demonstrate the effects of dependency parameters, initial surpluses, discounting factors on the aforementioned distributions. Moreover, the probability functions of those quantities under the ordinary model and the delayed model are compared. Subjects: Risk (Insurance) - Mathematical models
Author: Gordon E. Willmot
Author: Gordon E. Willmot
Author: Vsevolod K. Malinovskii
Author: Michel Mandjes
Author: Remigijus Leipus
Author: 
Author: Vladimir Panov
Author: 
Author: S. Ramasubramanian
Author: Xiaozhen Qi
Author: Edward L. Melnick