Semi-Markov Risk Models for Finance, Insurance and Reliability
Semi-Markov Risk Models for Finance, Insurance and Reliability
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DOI：
10.1007/0-387-70730-1
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发表时间：
2007-03
期刊：
影响因子：
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通讯作者：
J. Janssen;R. Manca
中科院分区：
文献类型：
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作者：
J. Janssen;R. Manca
这本书旨在给出具有有限多个状态的半马尔可夫模型的完整和自包含的表示，旨在解决金融、保险和可靠性三个主要领域的风险管理的现实问题，为我们的第一本书(Janssen和Manca(2006))提供了有用的补充，后者给出了半马尔可夫理论的理论表示。然而，为了帮助确保这本书是独立的，前三章提供了关于半马尔可夫理论的基本工具的概述，读者将需要这些工具来理解我们的演示文稿。关于更多细节，我们请读者参考我们的第一本书(Janssen and Manca(2006))，它的符号、定义和结果已经在这四个第一章中使用过。如今，如果没有好的计算机程序来处理相关数据，理论模型用于现实生活问题的潜力受到严重限制。因此，我们系统地提出了基本算法，以便得到有效的数值结果。这本书的另一个重要特点是它同时呈现了同质和非同质模型。众所周知，许多现实生活问题的基本结构在时间上是n齐次的，而应用齐次模型来解决这类问题，在最好的情况下，只能给出近似的结果，在最坏的情况下，只能给出无意义的结果。
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.