Semi-Markov Risk Models for Finance, Insurance and Reliability
Springer Science & Business Media, May 15, 2007 - Mathematics - 430 pages
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 n- homogeneous 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.
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AA A BBB AAA AA assumption asymptotic basic BB B CCC BBB BB Black and Scholes Brownian motion called Chapter compute conditional expectation conditional probability defined Definition discrete distribution function DTHSMP environment ergodic evolution equations example finite given gives ij ij independent interest rate introduce Janssen and Manca kernel Q Laplace transform Let us consider Markov chain Markov process Markov renewal martingale mean moreover non-homogeneous normal distribution notation obtain option parameters pension fund period possible present value probability space problem Proposition random variables random walk recurrent renewal process renewal theory represents the probability risk model ruin probability semi-Markov model semi-Markov process seniority sequence stochastic process suppose Table theorem total number transition matrix transition probabilities underlying asset vector λβ ω ω