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Ruin Probabilities

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Ruin Probabilities

Ruin Probabilities Book
Author : S?ren Asmussen,Hansj”rg Albrecher
Publisher : World Scientific
Release : 2010
ISBN : 9814282529
Language : En, Es, Fr & De

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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.

Ruin Probabilities

Ruin Probabilities Book
Author : S?ren Asmussen
Publisher : World Scientific
Release : 2000
ISBN : 9812779310
Language : En, Es, Fr & De

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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.

Asymptotic Ruin Probabilities for a Bivariate L vy Driven Risk Model with Heavy Tailed Claims and Risky Investments

Asymptotic Ruin Probabilities for a Bivariate L  vy Driven Risk Model with Heavy Tailed Claims and Risky Investments Book
Author : N.A
Publisher :
Release : 2018
ISBN :
Language : En, Es, Fr & De

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Book Description :

Abstract : Consider a general bivariate Lévy-driven risk model. The surplus process Y, starting with Y 0 = x > 0, evolves according to d Y t = Y t - d R t -d P t for t > 0, where P and R are two independent Lévy processes respectively representing a loss process in a world without economic factors and a process describing the return on investments in real terms. Motivated by a conjecture of Paulsen, we study the finite-time and infinite-time ruin probabilities for the case in which the loss process P has a Lévy measure of extended regular variation and the stochastic exponential of R fulfills a moment condition. We obtain a simple and unified asymptotic formula as x →∞, which confirms Paulsen's conjecture.

Ruin Probability in a Generalised Risk Process Under Rates of Interest with Homogenous Markov Chains

Ruin Probability in a Generalised Risk Process Under Rates of Interest with Homogenous Markov Chains Book
Author : N.A
Publisher :
Release : 2014
ISBN :
Language : En, Es, Fr & De

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Book Description :

Abstract: This article explores recursive and integral equations for ruin probabilities of generalised risk processes, under rates of interest with homogenous Markov chain claims and homogenous Markov chain premiums. We assume that claim and premium take a countable number of non-negative values. Generalised Lundberg inequalities for the ruin probabilities of these processes are derived via a recursive technique. Recursive equations for finite time ruin probabilities and an integral equation for the ultimate ruin probability are presented, from which corresponding probability inequalities and upper bounds are obtained. An illustrative numerical example is discussed.

Handbook of Data Visualization

Handbook of Data Visualization Book
Author : Chun-houh Chen,Wolfgang Karl Härdle,Antony Unwin
Publisher : Springer Science & Business Media
Release : 2007-12-18
ISBN : 9783540330370
Language : En, Es, Fr & De

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Book Description :

Visualizing the data is an essential part of any data analysis. Modern computing developments have led to big improvements in graphic capabilities and there are many new possibilities for data displays. This book gives an overview of modern data visualization methods, both in theory and practice. It details modern graphical tools such as mosaic plots, parallel coordinate plots, and linked views. Coverage also examines graphical methodology for particular areas of statistics, for example Bayesian analysis, genomic data and cluster analysis, as well software for graphics.

Loss Models

Loss Models Book
Author : Stuart A. Klugman,Harry H. Panjer,Gordon E. Willmot
Publisher : John Wiley & Sons
Release : 2013-08-29
ISBN : 1118573749
Language : En, Es, Fr & De

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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.

Non Life Insurance Mathematics

Non Life Insurance Mathematics Book
Author : Thomas Mikosch
Publisher : Springer Science & Business Media
Release : 2009-04-21
ISBN : 3540882332
Language : En, Es, Fr & De

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Book Description :

"Offers a mathematical introduction to non-life insurance and, at the same time, to a multitude of applied stochastic processes. It gives detailed discussions of the fundamental models for claim sizes, claim arrivals, the total claim amount, and their probabilistic properties....The reader gets to know how the underlying probabilistic structures allow one to determine premiums in a portfolio or in an individual policy." --Zentralblatt für Didaktik der Mathematik

Modern Actuarial Risk Theory

Modern Actuarial Risk Theory Book
Author : Rob Kaas,Marc Goovaerts,Jan Dhaene,Michel Denuit
Publisher : Springer Science & Business Media
Release : 2008-08-17
ISBN : 3540709983
Language : En, Es, Fr & De

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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 much expanded edition emphasizes the implementation of these techniques through the use of R. This free but incredibly powerful software is rapidly developing into the de facto standard for statistical computation, not just in academic circles but also in practice. With R, one can do simulations, find maximum likelihood estimators, compute distributions by inverting transforms, and much more.

Stochastic Processes for Insurance and Finance

Stochastic Processes for Insurance and Finance Book
Author : Tomasz Rolski,Hanspeter Schmidli,V. Schmidt,Jozef L. Teugels
Publisher : John Wiley & Sons
Release : 2009-09-25
ISBN : 0470317884
Language : En, Es, Fr & De

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Book Description :

Stochastic Processes for Insurance and Finance offers a thorough yet accessible reference for researchers and practitioners of insurance mathematics. Building on recent and rapid developments in applied probability, the authors describe in general terms models based on Markov processes, martingales and various types of point processes. Discussing frequently asked insurance questions, the authors present a coherent overview of the subject and specifically address: The principal concepts from insurance and finance Practical examples with real life data Numerical and algorithmic procedures essential for modern insurance practices Assuming competence in probability calculus, this book will provide a fairly rigorous treatment of insurance risk theory recommended for researchers and students interested in applied probability as well as practitioners of actuarial sciences. Wiley Series in Probability and Statistics

Fundamentals of Actuarial Mathematics

Fundamentals of Actuarial Mathematics Book
Author : S. David Promislow
Publisher : John Wiley & Sons
Release : 2014-11-26
ISBN : 1118782526
Language : En, Es, Fr & De

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Book Description :

Provides a comprehensive coverage of both the deterministic and stochastic models of life contingencies, risk theory, credibility theory, multi-state models, and an introduction to modern mathematical finance. New edition restructures the material to fit into modern computational methods and provides several spreadsheet examples throughout. Covers the syllabus for the Institute of Actuaries subject CT5, Contingencies Includes new chapters covering stochastic investments returns, universal life insurance. Elements of option pricing and the Black-Scholes formula will be introduced.

Modern Problems in Insurance Mathematics

Modern Problems in Insurance Mathematics Book
Author : Dmitrii Silvestrov,Anders Martin-Löf
Publisher : Springer
Release : 2014-06-06
ISBN : 3319066536
Language : En, Es, Fr & De

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Book Description :

This book is a compilation of 21 papers presented at the International Cramér Symposium on Insurance Mathematics (ICSIM) held at Stockholm University in June, 2013. The book comprises selected contributions from several large research communities in modern insurance mathematics and its applications. The main topics represented in the book are modern risk theory and its applications, stochastic modelling of insurance business, new mathematical problems in life and non-life insurance and related topics in applied and financial mathematics. The book is an original and useful source of inspiration and essential reference for a broad spectrum of theoretical and applied researchers, research students and experts from the insurance business. In this way, Modern Problems in Insurance Mathematics will contribute to the development of research and academy–industry co-operation in the area of insurance mathematics and its applications.

Encyclopedia of Actuarial Science

Encyclopedia of Actuarial Science Book
Author : Jozef L. Teugels,Jef L. Teugels,Bjørn Sundt
Publisher : John Wiley & Sons Incorporated
Release : 2004
ISBN :
Language : En, Es, Fr & De

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Book Description :

The Encyclopedia of Actuarial Science presents a timely and comprehensive body of knowledge designed to serve as an essential reference for the actuarial profession and all related business and financial activities, as well as researchers and students in actuarial science and related areas. Drawing on the experience of leading international editors and authors from industry and academic research the encyclopedia provides an authoritative exposition of both quantitative methods and practical aspects of actuarial science and insurance. The cross-disciplinary nature of the work is reflected not only in its coverage of key concepts from business, economics, risk, probability theory and statistics but also by the inclusion of supporting topics such as demography, genetics, operations research and informatics.

Insurance Risk and Ruin

Insurance Risk and Ruin Book
Author : David C. M. Dickson
Publisher : Cambridge University Press
Release : 2016-10-31
ISBN : 110715460X
Language : En, Es, Fr & De

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Book Description :

Balancing rigor and intuition, the new edition of this first course in risk theory has added exercises and expands on contemporary topics.

Statistical Tools for Finance and Insurance

Statistical Tools for Finance and Insurance Book
Author : Pavel Cizek,Wolfgang Karl Härdle,Rafał Weron
Publisher : Springer Science & Business Media
Release : 2005-12-06
ISBN : 9783540273950
Language : En, Es, Fr & De

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Book Description :

Written in an accessible and engaging style, this self-instructional book makes a good use of extensive examples and full explanations. The electronic edition, allowing the reader to run, modify, and enhance all quantlets on the spot, can be downloaded at no cost via the attached license registration card.