This book 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. Throughout the book the language of stochastic processes is used for describing the dynamics of an insurance portfolio in claim size space and time. In addition to the standard actuarial notions, the reader learns about the basic models of modern non-life insurance mathematics: the Poisson, compound Poisson and renewal processes in collective risk theory and heterogeneity and Bühlmann models in experience rating. The reader gets to know how the underlying probabilistic structures allow one to determine premiums in a portfolio or in an individual policy. Special emphasis is given to the phenomena which are caused by large claims in these models.What makes this book special are more than 100 figures and tables illustrating and visualizing the theory. Every section ends with extensive exercises. They are an integral part of this course since they support the access to the theory.The book can serve either as a text for an undergraduate/graduate course on non-life insurance mathematics or applied stochastic processes. Its content is in agreement with the European ''Group Consultatif'' standards. An extensive bibliography, annotated by various comments sections with references to more advanced relevant literature, make the book broadly and easiliy accessible.
The aim of this book is to bring some of the standard stochastic models of non-life insurance mathematics to the attention of a wide audience which, hopefully, will include actuaries and also other applied scientists. The primary objective of this book is to provide the undergraduate actuarial student with an introduction to non-life insurance mathematics.
The choice of topics presented in this book has been dictated, on the one hand, by personal taste and, on the other hand, by some practical considerations. This course is the basis for other courses in the curriculum of the Danish actuarial education and therefore it has to cover a certain variety of topics. This education is in agreement with the Groupe Consultatif requirements, which are valid in most European countries.
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