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An introduction to simulation of risk processes


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  • Krzysztof Burnecki
  • Wolfgang Hardle
  • Rafal Weron


A typical model for insurance risk, the so-called collective risk model, has two main components: one characterizing the frequency (or incidence) of events and another describing the severity (or size or amount) of gain or loss resulting from the occurrence of an event. Here we focus on simulating the point process N(t) of the incidence of events. We discuss five prominent examples of N(t), namely the classical (homogeneous) Poisson process, the non-homogeneous Poisson process, the mixed Poisson process, the Cox process (also called the doubly stochastic Poisson process) and the renewal process.

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Bibliographic Info

Paper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/03/04.

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Length: 9 pages
Date of creation: 2003
Date of revision:
Handle: RePEc:wuu:wpaper:hsc0304

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Related research

Keywords: Collective risk model; Poisson process; Non-homogeneous Poisson process; Mixed Poisson process; Cox process; Renewal process;

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Cited by:
  1. Chernobai, Anna & Burnecki, Krzysztof & Rachev, Svetlozar & Trueck, Stefan & Weron, Rafal, 2005. "Modelling catastrophe claims with left-truncated severity distributions (extended version)," MPRA Paper 10423, University Library of Munich, Germany.
  2. Weron, Rafał & Burnecki, Krzysztof, 2004. "Modeling the risk process in the XploRe computing environment," Papers 2004,08, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).


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