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Author: Tzvetan Ignatov Publisher: ISBN: Category : Languages : en Pages :
Book Description
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: Tzvetan Ignatov Publisher: ISBN: Category : Languages : en Pages :
Book Description
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: 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: N. Balakrishnan Publisher: Springer Science & Business Media ISBN: 0817644873 Category : Mathematics Languages : en Pages : 515
Book Description
The purpose of this book is to honor the fundamental contributions to many different areas of statistics made by Barry Arnold. Distinguished and active researchers highlight some of the recent developments in statistical distribution theory, order statistics and their properties, as well as inferential methods associated with them. Applications to survival analysis, reliability, quality control, and environmental problems are emphasized.
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: Thomas Mikosch Publisher: Springer Science & Business Media ISBN: 3540882332 Category : Mathematics Languages : en Pages : 435
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
Author: David F. Anderson Publisher: 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: Dimitri Bertsekas Publisher: Athena Scientific ISBN: 188652923X Category : Mathematics Languages : en Pages : 544
Book Description
An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.
Author: Michel Denuit Publisher: John Wiley & Sons ISBN: 9780470517413 Category : Mathematics Languages : en Pages : 384
Book Description
There are a wide range of variables for actuaries to consider when calculating a motorist’s insurance premium, such as age, gender and type of vehicle. Further to these factors, motorists’ rates are subject to experience rating systems, including credibility mechanisms and Bonus Malus systems (BMSs). Actuarial Modelling of Claim Counts presents a comprehensive treatment of the various experience rating systems and their relationships with risk classification. The authors summarize the most recent developments in the field, presenting ratemaking systems, whilst taking into account exogenous information. The text: Offers the first self-contained, practical approach to a priori and a posteriori ratemaking in motor insurance. Discusses the issues of claim frequency and claim severity, multi-event systems, and the combinations of deductibles and BMSs. Introduces recent developments in actuarial science and exploits the generalised linear model and generalised linear mixed model to achieve risk classification. Presents credibility mechanisms as refinements of commercial BMSs. Provides practical applications with real data sets processed with SAS software. Actuarial Modelling of Claim Counts is essential reading for students in actuarial science, as well as practicing and academic actuaries. It is also ideally suited for professionals involved in the insurance industry, applied mathematicians, quantitative economists, financial engineers and statisticians.
Author: Tzvetan Ignatov
Author: Tzvetan Ignatov
Author: 
Author: N. Balakrishnan
Author: 
Author: Edward L. Melnick
Author: S?ren Asmussen
Author: Thomas Mikosch
Author: David F. Anderson
Author: Dimitri Bertsekas
Author: Michel Denuit