Stochastic Methods For Life Insurance
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| Author | : Mario V. Wüthrich |
| Publisher | : John Wiley & Sons |
| Total Pages | : 438 |
| Release | : 2008-04-30 |
| Genre | : Business & Economics |
| ISBN | : 0470772727 |
Claims reserving is central to the insurance industry. Insurance liabilities depend on a number of different risk factors which need to be predicted accurately. This prediction of risk factors and outstanding loss liabilities is the core for pricing insurance products, determining the profitability of an insurance company and for considering the financial strength (solvency) of the company. Following several high-profile company insolvencies, regulatory requirements have moved towards a risk-adjusted basis which has lead to the Solvency II developments. The key focus in the new regime is that financial companies need to analyze adverse developments in their portfolios. Reserving actuaries now have to not only estimate reserves for the outstanding loss liabilities but also to quantify possible shortfalls in these reserves that may lead to potential losses. Such an analysis requires stochastic modeling of loss liability cash flows and it can only be done within a stochastic framework. Therefore stochastic loss liability modeling and quantifying prediction uncertainties has become standard under the new legal framework for the financial industry. This book covers all the mathematical theory and practical guidance needed in order to adhere to these stochastic techniques. Starting with the basic mathematical methods, working right through to the latest developments relevant for practical applications; readers will find out how to estimate total claims reserves while at the same time predicting errors and uncertainty are quantified. Accompanying datasets demonstrate all the techniques, which are easily implemented in a spreadsheet. A practical and essential guide, this book is a must-read in the light of the new solvency requirements for the whole insurance industry.
| Author | : Michael Koller |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 222 |
| Release | : 2012-03-22 |
| Genre | : Mathematics |
| ISBN | : 3642284396 |
The book provides a sound mathematical base for life insurance mathematics and applies the underlying concepts to concrete examples. Moreover the models presented make it possible to model life insurance policies by means of Markov chains. Two chapters covering ALM and abstract valuation concepts on the background of Solvency II complete this volume. Numerous examples and a parallel treatment of discrete and continuous approaches help the reader to implement the theory directly in practice.
| Author | : Tomasz Rolski |
| Publisher | : Wiley |
| Total Pages | : 0 |
| Release | : 2009-03-09 |
| Genre | : Mathematics |
| ISBN | : 9780470743638 |
The Wiley Paperback Series makes valuable content more accessible to a new generation of statisticians, mathematicians and scientists. 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 this subject and specifically address: the principle concepts of 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 rigorous treatment of insurance risk theory recommended for researchers and students interested in applied probability as well as practitioners of actuarial sciences. “An excellent text” Australian & New Zealand Journal of Statistics
| Author | : X. Sheldon Lin |
| Publisher | : John Wiley & Sons |
| Total Pages | : 224 |
| Release | : 2006-04-21 |
| Genre | : Mathematics |
| ISBN | : 0471793205 |
Incorporates the many tools needed for modeling and pricing infinance and insurance Introductory Stochastic Analysis for Finance and Insuranceintroduces readers to the topics needed to master and use basicstochastic analysis techniques for mathematical finance. The authorpresents the theories of stochastic processes and stochasticcalculus and provides the necessary tools for modeling and pricingin finance and insurance. Practical in focus, the book's emphasisis on application, intuition, and computation, rather thantheory. Consequently, the text is of interest to graduate students,researchers, and practitioners interested in these areas. While thetext is self-contained, an introductory course in probabilitytheory is beneficial to prospective readers. This book evolved from the author's experience as an instructor andhas been thoroughly classroom-tested. Following an introduction,the author sets forth the fundamental information and tools neededby researchers and practitioners working in the financial andinsurance industries: * Overview of Probability Theory * Discrete-Time stochastic processes * Continuous-time stochastic processes * Stochastic calculus: basic topics The final two chapters, Stochastic Calculus: Advanced Topics andApplications in Insurance, are devoted to more advanced topics.Readers learn the Feynman-Kac formula, the Girsanov's theorem, andcomplex barrier hitting times distributions. Finally, readersdiscover how stochastic analysis and principles are applied inpractice through two insurance examples: valuation of equity-linkedannuities under a stochastic interest rate environment andcalculation of reserves for universal life insurance. Throughout the text, figures and tables are used to help simplifycomplex theory and pro-cesses. An extensive bibliography opens upadditional avenues of research to specialized topics. Ideal for upper-level undergraduate and graduate students, thistext is recommended for one-semester courses in stochastic financeand calculus. It is also recommended as a study guide forprofessionals taking Causality Actuarial Society (CAS) and Societyof Actuaries (SOA) actuarial examinations.
| Author | : Michael Koller |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 222 |
| Release | : 2012-03-23 |
| Genre | : Mathematics |
| ISBN | : 3642284388 |
The book provides a sound mathematical base for life insurance mathematics and applies the underlying concepts to concrete examples. Moreover the models presented make it possible to model life insurance policies by means of Markov chains. Two chapters covering ALM and abstract valuation concepts on the background of Solvency II complete this volume. Numerous examples and a parallel treatment of discrete and continuous approaches help the reader to implement the theory directly in practice.
| Author | : Thomas Mikosch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 435 |
| Release | : 2009-04-21 |
| Genre | : Mathematics |
| ISBN | : 3540882332 |
"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 | : Tomasz Rolski |
| Publisher | : John Wiley & Sons |
| Total Pages | : 680 |
| Release | : 2009-09-25 |
| Genre | : Mathematics |
| ISBN | : 0470317884 |
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
| Author | : D N Shanbhag |
| Publisher | : Gulf Professional Publishing |
| Total Pages | : 990 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9780444500144 |
This volume in the series contains chapters on areas such as pareto processes, branching processes, inference in stochastic processes, Poisson approximation, Levy processes, and iterated random maps and some classes of Markov processes. Other chapters cover random walk and fluctuation theory, a semigroup representation and asymptomatic behavior of certain statistics of the Fisher-Wright-Moran coalescent, continuous-time ARMA processes, record sequence and their applications, stochastic networks with product form equilibrium, and stochastic processes in insurance and finance. Other subjects include renewal theory, stochastic processes in reliability, supports of stochastic processes of multiplicity one, Markov chains, diffusion processes, and Ito's stochastic calculus and its applications. c. Book News Inc.
| Author | : Søren Asmussen |
| Publisher | : Springer Nature |
| Total Pages | : 505 |
| Release | : 2020-04-17 |
| Genre | : Mathematics |
| ISBN | : 3030351769 |
This textbook provides a broad overview of the present state of insurance mathematics and some related topics in risk management, financial mathematics and probability. Both non-life and life aspects are covered. The emphasis is on probability and modeling rather than statistics and practical implementation. Aimed at the graduate level, pointing in part to current research topics, it can potentially replace other textbooks on basic non-life insurance mathematics and advanced risk management methods in non-life insurance. Based on chapters selected according to the particular topics in mind, the book may serve as a source for introductory courses to insurance mathematics for non-specialists, advanced courses for actuarial students, or courses on probabilistic aspects of risk. It will also be useful for practitioners and students/researchers in related areas such as finance and statistics who wish to get an overview of the general area of mathematical modeling and analysis in insurance.
| Author | : Michael Koller |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 345 |
| Release | : 2011-05-04 |
| Genre | : Business & Economics |
| ISBN | : 3642207219 |
The aim of the book is to provide an overview of risk management in life insurance companies. The focus is twofold: (1) to provide a broad view of the different topics needed for risk management and (2) to provide the necessary tools and techniques to concretely apply them in practice. Much emphasis has been put into the presentation of the book so that it presents the theory in a simple but sound manner. The first chapters deal with valuation concepts which are defined and analysed, the emphasis is on understanding the risks in corresponding assets and liabilities such as bonds, shares and also insurance liabilities. In the following chapters risk appetite and key insurance processes and their risks are presented and analysed. This more general treatment is followed by chapters describing asset risks, insurance risks and operational risks - the application of models and reporting of the corresponding risks is central. Next, the risks of insurance companies and of special insurance products are looked at. The aim is to show the intrinsic risks in some particular products and the way they can be analysed. The book finishes with emerging risks and risk management from a regulatory point of view, the standard model of Solvency II and the Swiss Solvency Test are analysed and explained. The book has several mathematical appendices which deal with the basic mathematical tools, e.g. probability theory, stochastic processes, Markov chains and a stochastic life insurance model based on Markov chains. Moreover, the appendices look at the mathematical formulation of abstract valuation concepts such as replicating portfolios, state space deflators, arbitrage free pricing and the valuation of unit linked products with guarantees. The various concepts in the book are supported by tables and figures.
