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An introduction to simulation of risk processes

Author

Listed:
  • Krzysztof Burnecki
  • Wolfgang Hardle
  • Rafal Weron

Abstract

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.

Suggested Citation

  • Krzysztof Burnecki & Wolfgang Hardle & Rafal Weron, 2003. "An introduction to simulation of risk processes," HSC Research Reports HSC/03/04, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    • Handle: RePEc:wuu:wpaper:hsc0304
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    File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_03_04.pdf
    File Function: Original version, 2003
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    Citations

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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 University of Berlin, Center for Applied Statistics and Economics (CASE).

    More about this item

    Keywords

    Collective risk model; Poisson process; Non-homogeneous Poisson process; Mixed Poisson process; Cox process; Renewal process;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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