الصفحة 1
الصفحة 1
Uncertainty Theory
Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, and countable subadditivity axioms. The goal of uncertainty theory is to study the behavior of uncertain phenomena such as fuzziness and randomness. The main topics include probability theory, credibility theory, and chance theory. For this new edition the entire text has been totally rewritten. More importantly, the chapters on chance theory and uncertainty theory are completely new. This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. Mathematicians, researchers, engineers, designers, and students in the field of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, and management science will find this work a stimulating and useful reference.
A Course in Credibility Theory and its Applications
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 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.for a first course on Credibility.
