Author: Ki-Lung KwokPublisher:
ISBN: 9781361043660
Category : Insurance
Languages : en
Pages : 112
Book Description
On Computing Ruin Probabilities
Author: Ki-Lung KwokPublisher:
ISBN: 9781361043660
Category : Insurance
Languages : en
Pages : 112
Book Description
Ruin Probabilities
Author: S?ren AsmussenPublisher: 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.
ON COMPUTING RUIN PROBABILITIE
Author: Ki-Lung KwokPublisher: Open Dissertation Press
ISBN: 9781361043783
Category : Mathematics
Languages : en
Pages : 68
Book Description
This dissertation, "On Computing Ruin Probabilities" by Ki-lung, Kwok, 郭麒龍, 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: The objective of this thesis is to develop for an effective numerical scheme to calculate the finite-time ruin probabilities (equivalently the finite-time survival probabilities) under classical risk model. Ruin theory of this model has been widely studied in literatures especially those related to ruin probabilities. However, in a lot of cases, numerical solutions are needed and so an efficient numerical scheme is in great demand. In this thesis, the survival probability is going to be evaluated via a very effective wavelets scheme. In 1997, Picard and Lefevre derived an explicit formula for survival probabilities in finite-time horizon for general Levy processes. However, in a lot of risk models, this formula involves infinitely many convolutions of a compound Poisson density function. Hence, evaluating it becomes very difficult. We shall combine a discretization with a wavelets expansion to achieve the evaluation task. Wavelets is a function basis that possesses a number of nice properties including compact supportness and this facilitates very efficient computations. Since its introduction, wavelets has attracted many researches and has been popular in solving PDEs and option pricing. As far as we know, wavelets method has not been applied to risk theory. It is new that wavelets expansion is used in computing survival probabilities. Our wavelets numerical scheme is direct and simple in computations. It also has a computational complexity of O(n) compared to that of O(n log n) via the typical methods, like Fast Fourier Transforms. An explicit error bound for our wavelets scheme is given with the help of Jackson's inequality. In Chapter 1, a brief review on the development of risk theory and the Picard- Lefevre formula on survival probability in finite-time horizon is presented, followed by a brief introduction of wavelets expansion and multi-resolution analysis in Chapter 2. An explicit error bound for the numerical approximation is provided in Chapter 3. Finally, numerical illustrations of the wavelets scheme are exhibited in Chapter 4. Subjects: Insurance - Mathematics Risk
Ruin Probabilities (2nd Edition)
Author: Soren AsmussenPublisher: 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.
Ruin Probabilities
Author: S?ren AsmussenPublisher: World Scientific
ISBN: 9812779310
Category : Mathematics
Languages : en
Pages : 399
Book Description
The text is a treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramer-Lundberg approximation, exact solutions, other approximations (for example, 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 computational vehicle and the connection to other applied probability areas like queueing theory.
On the Evaluation of Finite-Time Ruin Probabilities in a Dependent Risk Model
Author: Dimitrina DimitrovaPublisher:
ISBN:
Category :
Languages : en
Pages : 37
Book Description
This paper establishes some enlightening connections between the explicit formulas of the finite-time ruin probability established by Ignatov and Kaishev (2000, 2004) and Ignatov et al. (2001) for a risk model allowing dependence. The numerical properties of these formulas are investigated and efficient algorithms for computing ruin probability with prescribed accuracy are presented. Extensive numerical comparisons and examples are provided.Research on ruin probability beyond the classical risk model has intensified in recent years. More general ruin probability models assuming dependence between claim amounts and/or claim arrivals and non-linear aggregate premium income have been considered in the actuarial and applied probability literature. Such models are better suited to reflect the dependence in the arrival and severity of losses generated by portfolios of insurance policies. Exploring ruin probability theoretically and numerically, under these more general dependence assumptions, is of utmost importance within the Solvency II framework of internal insolvency-risk model building.
Ruin Probabilities
Author: Soren AsmussenPublisher: 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.
Ruin Probabilities
Author: Yuliya MishuraPublisher: 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
Introduction to Probability
Author: David F. AndersonPublisher: Cambridge University Press
ISBN: 110824498X
Category : Mathematics
Languages : en
Pages : 447
Book Description
This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
Author: Søren Asmussen