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.