Thomas Mikosch 
Non-Life Insurance Mathematics 
An Introduction with the Poisson Process

‘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

Table of Content

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.

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.