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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 25444.

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Date of creation: 2010
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Handle: RePEc:pra:mprapa:25444

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Keywords: Risk process; Claim arrival process; Homogeneous Poisson process (HPP); Non-homogeneous Poisson process (NHPP); Mixed Poisson process; Cox process; Renewal process.;

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References

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  1. Tse,Yiu-Kuen, 2009. "Nonlife Actuarial Models," Cambridge Books, Cambridge University Press, number 9780521764650, Fall.
  2. 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.
  3. Burnecki, Krzysztof & Weron, Rafal, 2010. "Simulation of Risk Processes," MPRA Paper 25444, University Library of Munich, Germany.
    • Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  4. 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.
  5. Hormann, W., 1993. "The transformed rejection method for generating Poisson random variables," Insurance: Mathematics and Economics, Elsevier, vol. 12(1), pages 39-45, February.
  6. 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.
  7. 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.
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Citations

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Cited by:
  1. Burnecki, Krzysztof & Weron, Rafal, 2010. "Simulation of Risk Processes," MPRA Paper 25444, University Library of Munich, Germany.
    • Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  2. Rafal Weron & Michael Bierbrauer & Stefan Trück, 2003. "Modeling electricity prices: jump diffusion and regime switching," HSC Research Reports HSC/03/01, Hugo Steinhaus Center, Wroclaw University of Technology.
  3. 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).
  4. Burnecki, Krzysztof & Misiorek, Adam & Weron, Rafal, 2010. "Loss Distributions," MPRA Paper 22163, University Library of Munich, Germany.
  5. Anna Chernobai & Krzysztof Burnecki & Svetlozar Rachev & Stefan Trueck & Rafal Weron, 2005. "Modeling catastrophe claims with left-truncated severity distributions (extended version)," HSC Research Reports HSC/05/01, Hugo Steinhaus Center, Wroclaw University of Technology.
  6. Wolfgang Härdle & Brenda López Cabrera, 2007. "Calibrating CAT bonds for Mexican earthquakes," SFB 649 Discussion Papers SFB649DP2007-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  7. Krzysztof Burnecki & Joanna Janczura & Rafal Weron, 2010. "Building Loss Models," HSC Research Reports HSC/10/03, Hugo Steinhaus Center, Wroclaw University of Technology.
  8. Krzysztof Burnecki & Rafal Weron, 2006. "Visualization tools for insurance risk processes," HSC Research Reports HSC/06/06, Hugo Steinhaus Center, Wroclaw University of Technology.

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