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Titlebook: Gerber–Shiu Risk Theory; Andreas E. Kyprianou Textbook 2013 Springer International Publishing Switzerland 2013 Cramér–Lundberg Processes.G

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书目名称Gerber–Shiu Risk Theory
编辑Andreas E. Kyprianou
视频video
概述Provides a self-contained and easy-to-read introduction to classical ruin theory.Includes recent developments in exotic ruin theory.Makes transparent the connection with the theory of spectrally negat
丛书名称EAA Series
图书封面Titlebook: Gerber–Shiu Risk Theory;  Andreas E. Kyprianou Textbook 2013 Springer International Publishing Switzerland 2013 Cramér–Lundberg Processes.G
描述.Motivated by the many and long-standing contributions of H. Gerber and E. Shiu, this book gives a modern perspective on the problem of ruin for the classical Cramér–Lundberg model and the surplus of an insurance company. The book studies martingales and path decompositions, which are the main tools used in analysing the distribution of the time of ruin, the wealth prior to ruin and the deficit at ruin. Recent developments in exotic ruin theory are also considered. In particular, by making dividend or tax payments out of the surplus process, the effect on ruin is explored..Gerber-Shiu Risk Theory. can be used as lecture notes and is suitable for a graduate course. Each chapter corresponds to approximately two hours of lectures..
出版日期Textbook 2013
关键词Cramér–Lundberg Processes; Gerber-Shiu Function; Lévy Processes; Ruin Theory
版次1
doihttps://doi.org/10.1007/978-3-319-02303-8
isbn_softcover978-3-319-02302-1
isbn_ebook978-3-319-02303-8Series ISSN 1869-6929 Series E-ISSN 1869-6937
issn_series 1869-6929
copyrightSpringer International Publishing Switzerland 2013
The information of publication is updating

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Scale Functions and Ruin Probabilities,order to establish our first results concerning the classical ruin problem. We introduce the so-called ., which will prove to be indispensable, both in this chapter and later, when describing various distributional features of the ruin problem.
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,The Gerber–Shiu Measure,ficit at ruin. We shall develop an idea from Chapter ., involving Bernoulli trials of excursions from the minimum, to provide an identity for the expected occupation measure until ruin of the Cramér–Lundberg process. This identity will then play a key role in identifying an expression for the Gerber
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Reflection Strategies,ection (or barrier) strategy consists of paying dividends out of the surplus in such a way that, for a fixed barrier .>0, any excess of the surplus above this level is instantaneously paid out. The key object of interest in this chapter is the present value of the dividends paid until ruin under for
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Refraction Strategies,arge ourselves with the task of providing identities for the probability of ruin as well as the expected present value of dividends paid until ruin. It turns out that all identities can be written in terms of the scale functions of two different processes. One scale function comes from the Cramér–Lu
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Refraction Strategies,t turns out that all identities can be written in terms of the scale functions of two different processes. One scale function comes from the Cramér–Lundberg process . and the other from the same Cramér–Lundberg process but with premium rate reduced by ..
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