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A Course In Credibility Theory And Its Applications

Author: Hans Bühlmann
Publisher: Springer Science & Business Media
ISBN: 354029273X
Size: 50.30 MB
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This book is ideal for practicing experts in particular actuaries in the field of property-casualty insurance, life insurance, reinsurance and insurance supervision, as well as teachers and students. It provides an exploration of Credibility Theory, covering most aspects of this topic from the simplest case to the most detailed dynamic model. The book closely examines the tasks an actuary encounters daily: estimation of loss ratios, claim frequencies and claim sizes.

A Course In Credibility Theory And Its Applications

Author: Hans Bühlmann
Publisher: Springer Science & Business Media
ISBN: 9783540257530
Size: 29.11 MB
Format: PDF, ePub
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The book is aimed at teachers and students as well as practising experts in the financial area, in particular at actuaries in the field of property-casualty insurance, life insurance, reinsurance and insurance supervision. Persons working in the wider world of finance will also find many relevant ideas and examples even though credibility methods have not yet been widely applied here. The text combines scientific rigour with direct practical applicability. It is based on courses given by the two authors at ETH Zürich. These courses have undergone considerable changes over time. "A Course in Credibility Theory and its Applications" is the final product of this evolution. It covers the subject of Credibility Theory extensively and includes most aspects of this topic from the simplest case to the most general dynamic model. The first four chapters contain plenty of material for a first course on Credibility. The whole text is intended as a full one year course at intermediate to advanced level. Credibility is a lifeless topic if it is not linked closely to practical applications. The book therefore treats explicitly the tasks which the actuary encounters in his daily work such as estimation of loss ratios, claim frequencies and claim sizes. The models are worked out in detail (including the estimation of structural parameters) so that they can immediately be applied in practice. Most exercises are based on real insurance data and real situations from practice and many of them have the characteristics of a case study. The extension to practical problems arising from the general area of finance is often quite straightforward. This book deserves a place on the bookshelf of every actuary and mathematician who works, teaches or does research in the area of insurance and finance.

Logic And Structure

Author: Dirk van Dalen
Publisher: Springer Science & Business Media
ISBN: 3662029626
Size: 30.85 MB
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New corrected printing of a well-established text on logic at the introductory level.

Qualitative Theory Of Planar Differential Systems

Author: Freddy Dumortier
Publisher: Springer Science & Business Media
ISBN: 9783540329022
Size: 25.62 MB
Format: PDF, Docs
View: 2018
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This book deals with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability. In the last two chapters the performant software tool P4 is introduced. From the start, differential systems are represented by vector fields enabling, in full strength, a dynamical systems approach. All essential notions, including invariant manifolds, normal forms, desingularization of singularities, index theory and limit cycles, are introduced and the main results are proved for smooth systems with the necessary specifications for analytic and polynomial systems.

A Course On Mathematical Logic

Author: Shashi Mohan Srivastava
Publisher: Springer Science & Business Media
ISBN: 1461457467
Size: 71.21 MB
Format: PDF, ePub
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This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more.

Fundamentals And Advanced Techniques In Derivatives Hedging

Author: Bruno Bouchard
Publisher: Springer
ISBN: 3319389904
Size: 23.76 MB
Format: PDF, ePub
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This book covers the theory of derivatives pricing and hedging as well as techniques used in mathematical finance. The authors use a top-down approach, starting with fundamentals before moving to applications, and present theoretical developments alongside various exercises, providing many examples of practical interest.A large spectrum of concepts and mathematical tools that are usually found in separate monographs are presented here. In addition to the no-arbitrage theory in full generality, this book also explores models and practical hedging and pricing issues. Fundamentals and Advanced Techniques in Derivatives Hedging further introduces advanced methods in probability and analysis, including Malliavin calculus and the theory of viscosity solutions, as well as the recent theory of stochastic targets and its use in risk management, making it the first textbook covering this topic. Graduate students in applied mathematics with an understanding of probability theory and stochastic calculus will find this book useful to gain a deeper understanding of fundamental concepts and methods in mathematical finance.

An Introduction To Sequential Dynamical Systems

Author: Henning Mortveit
Publisher: Springer Science & Business Media
ISBN: 9780387498799
Size: 65.65 MB
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This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory - equivalence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook.

Non Life Insurance Mathematics

Author: Thomas Mikosch
Publisher: Springer Science & Business Media
ISBN: 3540406506
Size: 60.76 MB
Format: PDF, Mobi
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"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

Tools For Computational Finance

Author: Rüdiger U. Seydel
Publisher: Springer
ISBN: 1447173384
Size: 22.14 MB
Format: PDF, Kindle
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Computational and numerical methods are used in a number of ways across the field of finance. It is the aim of this book to explain how such methods work in financial engineering. By concentrating on the field of option pricing, a core task of financial engineering and risk analysis, this book explores a wide range of computational tools in a coherent and focused manner and will be of use to anyone working in computational finance. Starting with an introductory chapter that presents the financial and stochastic background, the book goes on to detail computational methods using both stochastic and deterministic approaches. Now in its sixth edition, Tools for Computational Finance has been significantly revised and contains: Several new parts such as a section on extended applications of tree methods, including multidimensional trees, trinomial trees, and the handling of dividends; Additional material in the field of generating normal variates with acceptance-rejection methods, and on Monte Carlo methods; 115 exercises, and more than 100 figures, many in color. Written from the perspective of an applied mathematician, all methods are introduced for immediate and straightforward application. A ‘learning by calculating’ approach is adopted throughout this book, enabling readers to explore several areas of the financial world. Interdisciplinary in nature, this book will appeal to advanced undergraduate and graduate students in mathematics, engineering, and other scientific disciplines as well as professionals in financial engineering.

A Course In Large Sample Theory

Author: Thomas S. Ferguson
Publisher: Routledge
ISBN: 1351470051
Size: 65.69 MB
Format: PDF, Kindle
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A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study.