Non-Life Insurance Mathematics: An Introduction with Stochastic Processes (Universitext) - Softcover

Mikosch, Thomas

Softcover

ISBN 10: 3540406506 ISBN 13: 9783540406501

Publisher: Springer, 2006

Synopsis

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 "Groupe Consultatif" standards. An extensive bibliography, annotated by various comments sections with references to more advanced relevant literature, make the book broadly and easiliy accessible.

About this title

From the Back Cover

The volume offers a mathematical introduction to non-life insurance and, at the same time, to a multitude of applied stochastic processes. It includes detailed discussions of the fundamental models regarding claim sizes, claim arrivals, the total claim amount, and their probabilistic properties. Throughout the volume the language of stochastic processes is used for describing the dynamics of an insurance portfolio in claim size, space and time. Special emphasis is given to the phenomena which are caused by large claims in these models. The reader learns how the underlying probabilistic structures allow determining premiums in a portfolio or in an individual policy.

The second edition contains various new chapters that illustrate the use of point process techniques in non-life insurance mathematics. Poisson processes play a central role. Detailed discussions show how Poisson processes can be used to describe complex aspects in an insurance business such as delays in reporting, the settlement of claims and claims reserving. Also the chain ladder method is explained in detail.

More than 150 figures and tables illustrate and visualize the theory. Every section ends with numerous exercises. An extensive bibliography, annotated with various comments sections with references to more advanced relevant literature, makes the volume broadly and easily accessible.

About the Author

Thomas Mikosch has been professor at the Laboratory of Actuarial Mathematics of the University of Copenhagen since January 2001. Before this, he held positions in Dresden (Germany), Wellington (New Zealand) and Groningen (Netherlands). His special interests are applied probability theory and stochastic processes. Over the last few years his research has focused on extremal events in finance, insurance and telecommunications. His earlier very successful book, written jointly with Paul Embrechts and Claudia Klüppelberg, Modelling Extremal Events for Finance and Insurance (1997), is also published by Springer.

Edition details

• Publisher: Springer
• Publication date: 2006
• Language: English
• ISBN 10: 3540406506
• ISBN 13: 9783540406501
• Binding: Paperback
• Edition number: 2
• Number of pages: 235