On Numerical Evaluation of Finite Time Ruin Probabilities PDF Download

Author: David C. M. Dickson
Publisher:
ISBN:
Category : Risk (Insurance)
Languages : en
Pages : 16

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Author: Dimitrina Dimitrova
Publisher:
ISBN:
Category :
Languages : en
Pages : 37

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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.

Author: S?ren Asmussen
Publisher: World Scientific
ISBN: 9814282529
Category : Mathematics
Languages : en
Pages : 621

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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 Cram‚r?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: Tzvetan Ignatov
Publisher:
ISBN:
Category :
Languages : en
Pages :

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An improved version of a ruin probability formula due to Ignatov and Kaishev [Scand. Actu. J. 1 (2000) 46], allowing for the exact evaluation of the finite-time survival probability for discrete, dependent, individual claims, Poisson claim arrivals and arbitrary, increasing premium income function is derived. Its numerical efficiency is studied, using the Mathematica system. Numerical results are provided and computational aspects are discussed. A Mathematica module, realizing the Picard and Lefegrave;vre [Scand. Actu. J. 1 (1997) 58] formula has also been developed and used for numerical investigations.

Author: Soren Asmussen
Publisher: World Scientific
ISBN: 9814500321
Category : Mathematics
Languages : en
Pages : 399

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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: Ki-Lung Kwok
Publisher: Open Dissertation Press
ISBN: 9781361043783
Category : Mathematics
Languages : en
Pages : 68

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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

Author: Yuliya Mishura
Publisher: Elsevier
ISBN: 0081020988
Category : Mathematics
Languages : en
Pages : 278

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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:
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 430

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Book Description

Author: Stuart A. Klugman
Publisher: John Wiley & Sons
ISBN: 1118343565
Category : Business & Economics
Languages : en
Pages : 368

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Book Description
An essential resource for constructing and analyzing advanced actuarial models Loss Models: Further Topics presents extended coverage of modeling through the use of tools related to risk theory, loss distributions, and survival models. The book uses these methods to construct and evaluate actuarial models in the fields of insurance and business. Providing an advanced study of actuarial methods, the book features extended discussions of risk modeling and risk measures, including Tail-Value-at-Risk. Loss Models: Further Topics contains additional material to accompany the Fourth Edition of Loss Models: From Data to Decisions, such as: Extreme value distributions Coxian and related distributions Mixed Erlang distributions Computational and analytical methods for aggregate claim models Counting processes Compound distributions with time-dependent claim amounts Copula models Continuous time ruin models Interpolation and smoothing The book is an essential reference for practicing actuaries and actuarial researchers who want to go beyond the material required for actuarial qualification. Loss Models: Further Topics is also an excellent resource for graduate students in the actuarial field.

Author: David D. Hanagal
Publisher: Springer Nature
ISBN: 9811679320
Category : Mathematics
Languages : en
Pages : 318

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Book Description
This book collects select contributions presented at the International Conference on Importance of Statistics in Global Emerging (ISGES 2020) held at the Department of Mathematics and Statistics, University of Pune, Maharashtra, India, from 2–4 January 2020. It discusses recent developments in several areas of statistics with applications of a wide range of key topics, including small area estimation techniques, Bayesian models for small areas, ranked set sampling, fuzzy supply chain, probabilistic supply chain models, dynamic Gaussian process models, grey relational analysis and multi-item inventory models, and more. The possible use of other models, including generalized Lindley shared frailty models, Benktander Gibrat risk model, decision-consistent randomization method for SMART designs and different reliability models are also discussed. This book includes detailed worked examples and case studies that illustrate the applications of recently developed statistical methods, making it a valuable resource for applied statisticians, students, research project leaders and practitioners from various marginal disciplines and interdisciplinary research.