Semi-Markov Risk Models for Finance, Insurance and Reliability

This book aims to give a complete and self-contained presentation of semi- Markov models with finitely many states, in view of solving real life problems of risk management in three main fields: Finance, Insurance and Reliability providing a useful complement to our first book (Janssen and Manca (2006))

which gives a theoretical presentation of semi-Markov theory. However, to help assure the book is self-contained, the first three chapters provide a summary of the basic tools on semi-Markov theory that the reader will need to understand our presentation. For more details, we refer the reader to our first book (Janssen and Manca (2006)) whose notations, definitions and results have been used in these four first chapters.

Nowadays, the potential for theoretical models to be used on real-life problems is severely limited if there are no good computer programs to process the relevant data. We therefore systematically propose the basic algorithms so that effective numerical results can be obtained. Another important feature of this book is its presentation of both homogeneous and non-homogeneous models. It is well known that the fundamental structure of many real-life problems is nonhomogeneous in time, and the application of homogeneous models to such problems gives, in the best case, only approximated results or, in the worst case, nonsense results.

This book addresses a very large public as it includes undergraduate and graduate students in mathematics and applied mathematics, in economics and business studies, actuaries, financial intermediaries, engineers and operation researchers, but also researchers in universities and rd departments of banking, insurance and industry.

Readers who have mastered the material in this book will see how the classical models in our three fields of application can be extended in a semi-Markov environment to provide better new models, more general and able to solve problems in a more adapted way. They will indeed have a new approach giving a

more competitive knowledge related to the complexity of real-life problems.

Let us now give some comments on the contents of the book. As we start from the fact that the semi-Markov processes are the children of a successful marriage between renewal theory and Markov chains, these two topics are presented in Chapter 2. The full presentation of Markov renewal theory, Markov random walks and semi-Markov processes, functionals of (J-X) processes and semi-Markov random

walks is given in Chapter 3 along with a short presentation of non-homogeneous Markov and semi-Markov processes.

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