Paper: arXiv 2410.04369

Authors: 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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper makes a solid theoretical contribution by extending Voronoi residuals to deviance Voronoi residuals for spatio-temporal point processes. It demonstrates strong empirical rigor through practical applications to Canadian earthquake insurance risk, offering both a realistic MCT formula alternative and a fully reproducible, interactive web application.

Research Flowchart

  flowchart TD
    A["Research Goal: Improve Earthquake Insurance Risk & Minimum Capital Test (MCT) Modeling"] --> B["Data Inputs: Canadian Seismic Hazard Maps & Historical Earthquake Data"]
    B --> C["Extend Deviance Voronoi Residuals for Spatio-Temporal Point Process Models"]
    C --> D["Monte Carlo Simulation: Simulate Damage, Claim Payments & Provincial Correlation"]
    D --> E["Interactive Web App for Damage/Loss Simulation"]
    D --> F["New Country-Wide MCT Formula Accounting for Spatial Correlation"]

Cited References (73)

  1. Fifth Generation Seismic Hazard Model for Canada: Grid Values of Mean Hazard to be used with the 2015 National Building Code of Canada (2015)
  2. Relationships between Peak Ground Acceleration, Peak Ground Velocity, and Modified Mercalli Intensity in California (1999)
  3. Bounds on Kendall’s Tau for Zero-inflated Continuous Variables (2017)
  4. Association of Zero-inflated Continuous Variables (2015)
  5. Regional Seismic Risk in British Columbia - Damage and Loss Distribution in Victoria and Vancouver (2005)
  6. Census Profile, 2016 Census (2016)
  7. Canadian Housing Statistics Program (CHSP) (2020) — link
  8. Population Ecumene Census Division Cartographic Boundary File, Reference Guide, 2016 Census (2017) — link
and 65 more
  1. Multi-hazard Loss Estimation Methodology: Earthquake Model Hazus-MH 2.1 Technical Manual (2013)
  2. Statistical Inference Using Extreme Order Statistics (1975)
  3. Cool Earthquake Facts (2021) — link
  4. Earthquakes in Southeastern Canada (2011) — link
  5. Earthquakes in Southwestern British Columbia (2011) — link
  6. Economic Losses, Poverty and Disasters 1998-2017 (2017)
  7. HAZUS-MH 2.1 Canada User and Technical Manual: Earthquake Module (2014)
  8. Estimating Earthquake Location and Magnitude from Seismic Intensity Data (1997)
  9. Estimating Locations and Magnitudes of Earthquakes in Eastern North America from Modified Mercalli Intensities (2003)
  10. Nonparametric Estimation of Spatial Segregation in a Multivariate Point Process: Bovine Tuberculosis in Cornwall, UK (2005)
  11. A Kernel Method for Smoothing Point Process Data (1985)
  12. Density Estimation for Statistics and Data Analysis (1986)
  13. RSMeans Data: Construction Cost Estimating Software — link
  14. Table 18-10-0135-02 Building Construction Price Indexes, Percentage Change, Quarterly (2020) — link
  15. Table 34-10-0066-01 Building Permits, by Type of Structure and Type of Work (2020) — link
  16. Stochastic Declustering of Space-time Earthquake Occurrences (2002)
  17. Space-Time Point-Process Models for Earthquake Occurrences (1998)
  18. Point Processes (1980)
  19. An Introduction to the Theory of Point Processes Volume 1: Elementary Theory and Methods (2003)
  20. Statistical Inference and Simulation for Spatial Point Processes (2003)
  21. Statistical Analysis of Spatial and Spatio-temporal Point Patterns (2013)
  22. Statistics for Spatial Data (2015)
  23. Spatial Point Patterns: Methodology and Applications with R (2015)
  24. Can You Predict Earthquakes? — link
  25. Where do earthquakes occur? (2022) — link
  26. Key Figures Related to the Insurance Claims Paid for Earthquakes in Fiscal 2020 as of April 16, 2021 (2021) — link
  27. Frequently Asked Questions about Earthquakes (FAQ), How often do earthquakes occur in Canada? (2019) — link
  28. An Introduction to Statistical Modeling of Extreme Values (2001)
  29. Significant Canadian Earthquakes 1600-2017 (2018)
  30. Facts + Statistics: Earthquakes and Tsunamis (2021) — link
  31. Minimum Capital Test For Federally Regulated Property and Casualty Insurance Companies (2019) — link
  32. Commission Delegated Regulation (EU) 2015/ 35 of 10 October 2014 Supplementing Directive 2009/138/EC of the European Parliament and of the Council on the Taking-up and Pursuit of the Business of Insurance and Reinsurance (Solvency II) — link
  33. Study of Impact and the Insurance and Economic Cost of a Major Earthquake in British Columbia and Ontario/Qu 'e bec (2013)
  34. Earthquake Risk in Eastern Canada: Mind the Shakes (2017) — link
  35. Modified Mercalli Intensity Scale of 1931 (1931)
  36. Limiting Forms of the Frequency Distribution of the Largest or Smallest Member of a Sample (1928)
  37. The Frequency Distribution of the Annual Maximum (or Minimum) Values of Meteorological Elements (1955)
  38. La distribution de la plus grande de n valeurs (1954)
  39. A Methodology for Assessing the Seismic Risk of Buildings (2008)
  40. ATC-13: Earthquake Damage Evaluation for California (1985)
  41. Generalized P areto fit to the S ociety of A ctuaries’ L arge C laims D atabase (2003)
  42. Estimating Probable Maximum Loss with Order Statistics (1982)
  43. On the Probable Maximum Loss (1990)
  44. More on the Probable Maximum Loss (1994)
  45. East vs West Coast Earthquakes: U.S.@ Geological Survey (2018) — link
  46. Canada’s Loss and Exposure Indices Provider (2021) — link
  47. Qu'ebec is Resilient and Confident - Budget Plan (2021) — link
  48. Residual Analysis for Spatial Point Processes (with discussion) (2005)
  49. Second-order Residual Analysis of Spatiotemporal Point Processes and Applications in Model Evaluation (2006)
  50. On Mainshock Focal Mechanisms and the Spatial Distribution of Aftershocks (2009)
  51. Properties of Residuals for Spatial Point Processes (2008)
  52. Evaluation of Space-time Point Process Models Using Super-thinning (2012)
  53. Voronoi Residual Analysis of Spatial Point Process Models with Applications to California Earthquake Forecasts (2014)
  54. Spatial Tessellations (1999)
  55. Voronoi Residuals and Other Residual Analyses Applied to CSEP Earthquake Forecasts (2015)
  56. spatstat : An R Package for Analyzing Spatial Point Patterns (2005) — link
  57. R: A Language and Environment for Statistical Computing (2022) — link
  58. splancs: Spatial and Space-Time Point Pattern Analysis (2022) — link
  59. deldir: Delaunay Triangulation and Dirichlet (Voronoi) Tessellation (2021) — link
  60. stpp: Space-Time Point Pattern Simulation, Visualisation and Analysis (2022) — link
  61. Overview of the Working Group for the Development of Regional Earthquake Likelihood Models (RELM) (2007)
  62. Earthquake Predictability, Brick by Brick (2006)
  63. Efficient Testing of Earthquake Forecasting Models (2011)
  64. Likelihood-based Tests for Evaluating Space-rate-magnitude Earthquake Forecasts (2010)
  65. Earthquake Likelihood Model Testing (2007)

0 of 73 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.