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One is for claim reserving ,the other one for nonlife insurance mathematics.
Below is the related preface of the book:
To the outside world, insurance mathematics does not appear as a challenging
topic. In fact, everyone has to deal with matters of insurance at various
times of one’s life. Hence this is quite an interesting perception of a field
which constitutes one of the bases of modern society. There is no doubt that
modern economies and states would not function without institutions which
guarantee reimbursement to the individual, the company or the organization
for its losses, which may occur due to natural or man-made catastrophes,
fires, floods, accidents, riots, etc. The idea of insurance is part of our civilized
world. It is based on the mutual trust of the insurer and the insured.
It was realized early on that this mutual trust must be based on science,
not on belief and speculation. In the 20th century the necessary tools for
dealing with matters of insurance were developed. These consist of probability
theory, statistics and stochastic processes. The Swedish mathematicians
Filip Lundberg and Harald Cram´er were pioneers in these areas. They realized
in the first half of the 20th century that the theory of stochastic processes provides
the most appropriate framework for modeling the claims arriving in an
insurance business. Nowadays, the Cram´er-Lundberg model is one of the backbones
of non-life insurance mathematics. It has been modified and extended
in very different directions and, moreover, has motivated research in various
other fields of applied probability theory, such as queuing theory, branching
processes, renewal theory, reliability, dam and storage models, extreme value
theory, and stochastic networks.
The aim of this book is to bring some of the standard stochastic models
of non-life insurance mathematics to the attention of a wide audience which,
hopefully, will include actuaries and also other applied scientists. The primary
objective of this book is to provide the undergraduate actuarial student with
an introduction to non-life insurance mathematics. I used parts of this text in
the course on basic non-life insurance for 3rd year mathematics students at the
Laboratory of Actuarial Mathematics of the University of Copenhagen. But
I am convinced that the content of this book will also be of interest to others
who have a background on probability theory and stochastic processes and
would like to learn about applied stochastic processes. Insurance mathematics
is a part of applied probability theory. Moreover, its mathematical tools are
also used in other applied areas (usually under different names).
The idea of writing this book came in the spring of 2002, when I taught
basic non-life insurance mathematics at the University of Copenhagen. My
handwritten notes were not very much appreciated by the students, and so I
decided to come up with some lecture notes for the next course given in spring,
2003. This book is an extended version of those notes and the associated
weekly exercises. I have also added quite a few computer graphics to the
text. Graphs help one to understand and digest the theory much easier than
formulae and proofs. In particular, computer simulations illustrate where the
limits of the theory actually are.
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