# Non Life Insurance Mathematics

*Summer 2023*

# Preface

Risk aversion, or “riskphobia”, has become a virtue, as evidenced by the debates surrounding the precautionary principle. An abstract norm with ill-defined content, it is destined to become part of the preamble to our Constitution, at the risk of producing effects whose scope we have yet to measure.

In this context of uncertainty, it is particularly comforting to go back to basics, i.e. to mathematics, and to remember that risk arises from randomness and can be apprehended thanks to the most advanced developments in the calculation of probabilities.

This is precisely what Michel Denuit and Arthur Charpentier’s book “*Mathematics of non-life insurance*” reminds us of, and readers will appreciate its rigorous, clear and instructive presentation of modern risk analysis tools.

As an insurer, I was particularly struck by the introduction to copula theory, which allows us to model the dependence between the different risks faced by managers in our companies. After all, when disasters strike, losses are not independent.

I’m sure that this book will become an essential reference for actuaries. But beyond the narrow confines of the insurance sector, given the increasingly important place occupied by the idea of “risk” in our societies, the teaching of probability calculus in our engineering, business and management schools - and even in political science! -would benefit from tackling concrete risk management problems borrowed from actuarial science. This book provides the theoretical tools to do just that.

Future managers and decision-makers will be better able to integrate into their approach the fact that risk, properly quantified and appreciated, is also, if not more, an opportunity for innovation, a source of wealth creation, and therefore of progress for our societies.

**Claude Bébéar**, March 31st 2003.

This document is based on the two following books, (Denuit and Charpentier 2004) and (Denuit and Charpentier 2005), initially published in French.

### References

*Mathématiques de l’assurance Non-Vie, Tome 1*. Economica.

*Mathématiques de l’assurance Non-Vie, Tome 2*. Economica.