Abstract
In this chapter, we introduce some concepts that we shall apply later in the book, restricted to concepts needed in the univariate setting of Part I, covering notation and conventions, classes of distributions and functions, convolutions, mixed and compound distributions, moments, cumulants, (probability) generating functions, moment generating functions, characteristic functions, Laplace transforms, cumulant generating functions, some operators (in particular the cumulation operator and the tail operator), stop loss premiums, and convergence of infinite series with positive terms. Furthermore, we give an introduction to univariate aggregate claims distributions in insurance.
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© 2009 Springer-Verlag Berlin Heidelberg
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Sundt, B., Vernic, R. (2009). Introduction. In: Recursions for Convolutions and Compound Distributions with Insurance Applications. EAA Lecture Notes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92900-0_1
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DOI: https://doi.org/10.1007/978-3-540-92900-0_1
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92899-7
Online ISBN: 978-3-540-92900-0
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