Non-Life Insurance Mathematics

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.

Collective Risk Models.- The Basic Model.- Models for the Claim Number Process.- The Total Claim Amount.- Ruin Theory.- Experience Rating.- Bayes Estimation.- Linear Bayes Estimation.- A Point Process Approach to Collective Risk Theory.- The General Poisson Process.- Poisson Random Measures in Collective Risk Theory.- Weak Convergence of Point Processes.- Special Topics.- An Excursion to L#x00E9;vy Processes.- Cluster Point Processes.

From the reviews:

"The 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. ... 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." (Zentralblatt für Didaktik der Mathematik, November, 2004)

"The author's aim to bring some of the standard stochastic models of non-life insurance mathematics to the attention of a wide audience ... can definitely be reached by this textbook. It is well-written ... . Many figures and tables in this book help in illustrating and visualizing the developed theory. Moreover, every section ends with an extensive collection of exercises... and should help the reader in accessing the theory." (Josef Steinebach, Zentralblatt MATH, Vol. 1033 (8), 2004)

From the reviews of the second edition:

"The brief summary of the book's contents and purpose ... describes it as a mathematical introduction to non-life insurance, and it introduces the appropriate range of stochastic processes for this purpose. ... The book is based upon lectures given to 3^rd year mathematics students ... . this book is suited to study at the advanced undergraduate level at the earliest. Overall, this is a fascinating book on a subject ... ." (P. N. Ruane, The Mathematical Association of America, August, 2009)

"The book contains both basic and more advanced material on non-life insurance mathematics. ... aim at the undergraduate actuarical students. ... can serve as an independent course on stochastic models of non-life insurance mathematics at the graduate level." (Alexandra Rodkina, Zentralblatt MATH, Vol. 1166, 2009)