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Deviance Voronoi Residuals for Space-Time Point Process Models: An Application to Earthquake Insurance Risk

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  • Roba Bairakdar
  • Debbie Dupuis
  • Melina Mailhot

Abstract

Insurance risk arising from catastrophes such as earthquakes a component of the Minimum Capital Test for federally regulated property and casualty insurance companies. Analyzing earthquake insurance risk requires well-fitted spatio-temporal point process models. Given the spatial heterogeneity of earthquakes, the ability to assess whether the fits are adequate in certain locations is crucial in obtaining usable models. Accordingly, we extend the use of Voronoi residuals to calculate deviance Voronoi residuals. We also create a simulation-based approach, in which losses and insurance claim payments are calculated by relying on earthquake hazard maps of Canada. As an alternative to the current guidelines of OSFI, a formula to calculate the country-wide minimum capital test is proposed based on the correlation between the provinces. Finally, an interactive web application is provided which allows the user to simulate earthquake damage and the resulting financial losses and insurance claims, at a chosen epicenter location.

Suggested Citation

  • Roba Bairakdar & Debbie Dupuis & Melina Mailhot, 2024. "Deviance Voronoi Residuals for Space-Time Point Process Models: An Application to Earthquake Insurance Risk," Papers 2410.04369, arXiv.org.
    • Handle: RePEc:arx:papers:2410.04369
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    References listed on IDEAS

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    1. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
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    3. Peter Diggle, 1985. "A Kernel Method for Smoothing Point Process Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(2), pages 138-147, June.
    4. A. Baddeley & R. Turner & J. Møller & M. Hazelton, 2005. "Residual analysis for spatial point processes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 617-666, November.
    5. Zhuang J. & Ogata Y. & Vere-Jones D., 2002. "Stochastic Declustering of Space-Time Earthquake Occurrences," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 369-380, June.
    6. Jiancang Zhuang, 2006. "Second‐order residual analysis of spatiotemporal point processes and applications in model evaluation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 635-653, September.
    7. Baddeley, Adrian & Turner, Rolf, 2005. "spatstat: An R Package for Analyzing Spatial Point Patterns," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i06).
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