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Simulation of Risk Processes

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  • Burnecki, Krzysztof
  • Weron, Rafal

Abstract

This paper is intended as a guide to simulation of risk processes. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another describing the severity (or size) of loss resulting from the occurrence of a claim. The collective risk model is often used in health insurance and in general insurance, whenever the main risk components are the number of insurance claims and the amount of the claims. It can also be used for modeling other non-insurance product risks, such as credit and operational risk. In this paper we present efficient simulation algorithms for several classes of claim arrival processes.

Suggested Citation

  • Burnecki, Krzysztof & Weron, Rafal, 2010. "Simulation of Risk Processes," MPRA Paper 25444, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:25444
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    File URL: https://mpra.ub.uni-muenchen.de/25444/2/MPRA_paper_25444.pdf
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    Other versions of this item:

    • Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).

    References listed on IDEAS

    as
    1. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
    2. Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    3. Tse,Yiu-Kuen, 2009. "Nonlife Actuarial Models," Cambridge Books, Cambridge University Press, number 9780521764650, December.
    4. Burnecki, Krzysztof & Kukla, Grzegorz & Weron, Rafał, 2000. "Property insurance loss distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 269-278.
    5. Anna Chernobai & Krzysztof Burnecki & Svetlozar Rachev & Stefan Trück & Rafał Weron, 2006. "Modelling catastrophe claims with left-truncated severity distributions," Computational Statistics, Springer, vol. 21(3), pages 537-555, December.
    6. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
    7. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, December.
    8. Hormann, W., 1993. "The transformed rejection method for generating Poisson random variables," Insurance: Mathematics and Economics, Elsevier, vol. 12(1), pages 39-45, February.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Weron, R & Bierbrauer, M & Trück, S, 2004. "Modeling electricity prices: jump diffusion and regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 39-48.
    2. Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    3. Krzysztof Burnecki & Rafal Weron, 2006. "Visualization tools for insurance risk processes," HSC Research Reports HSC/06/06, Hugo Steinhaus Center, Wroclaw University of Technology.
    4. Borovkova, Svetlana & Schmeck, Maren Diane, 2017. "Electricity price modeling with stochastic time change," Energy Economics, Elsevier, vol. 63(C), pages 51-65.
    5. 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.
    6. Krzysztof Burnecki & Joanna Janczura & Rafal Weron, 2010. "Building Loss Models," HSC Research Reports HSC/10/03, Hugo Steinhaus Center, Wroclaw University of Technology.
    7. 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).
    8. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0601.
    9. Burnecki, Krzysztof & Misiorek, Adam & Weron, Rafal, 2010. "Loss Distributions," MPRA Paper 22163, University Library of Munich, Germany.
    10. Wolfgang Karl Härdle & Brenda López Cabrera, 2010. "Calibrating CAT Bonds for Mexican Earthquakes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(3), pages 625-650, September.
    11. A. Christian Silva & Ju-Yi Yen, 2010. "Stochastic resonance and the trade arrival rate of stocks," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 461-466.

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    More about this item

    Keywords

    Risk process; Claim arrival process; Homogeneous Poisson process (HPP); Non-homogeneous Poisson process (NHPP); Mixed Poisson process; Cox process; Renewal process.;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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