This textbook provides a broad overview of the present state of insurance mathematics and some related topics in risk management, financial mathematics and probability. Both non-life and life aspects are covered. The emphasis is on probability and modeling rather than statistics and practical implementation. Aimed at the graduate level, pointing in part to current research topics, it can potentially replace other textbooks on basic non-life insurance mathematics and advanced risk management methods in non-life insurance. Based on chapters selected according to the particular topics in mind, the book may serve as a source for introductory courses to insurance mathematics for non-specialists, advanced courses for actuarial students, or courses on probabilistic aspects of risk. It will also be useful for practitioners and students/researchers in related areas such as finance and statistics who wish to get an overview of the general area of mathematical modeling and analysis in insurance.

Autorentext

Søren Asmussen obtained his PhD at the University of Copenhagen in 1978, followed by the Danish degree of Dr. scient. in 1982. He held academic positions at the University of Copenhagen before moving to Aalborg University in 1987, where he received one of the prestigious Danish research professorships in 1990. In 1995, he became Professor of Mathematical Statistics at Lund University in Sweden, and then moved to his current position as Professor of Applied Probability at Aarhus University in Denmark in 2003. He received the Marcel F. Neuts Applied Probability Prize in 1999, the INFORMS Outstanding Publication Prizes in Simulation in 2002 and 2008, the John von Neumann Theory Prize in 2010, and the gold medal "For Great Contributions in Mathematics" from the Sobolev Institute of Mathematics, Russian Academy of Sciences in 2011.

Mogens Steffensen, University of Copenhagen

Inhalt

Basics.- Experience Rating.- Sums and Aggregate Claims.- Ruin Theory.- Markov Models in Life Insurance.- Financial Mathematics in Life Insurance.- Special Studies in Life Insurance.- Orderings and Comparisons.- Extreme Value Theory.- Dependence and Further Topics in Risk Management.- Stochastic Control in Non-Life Insurance.- Stochastic Control in Life Insurance.- Selected Further Topics.