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Direct and Hierarchical Models for Aggregating Spatially Dependent Catastrophe Risks

Author

Listed:
  • Rafał Wójcik

    (AIR-Worldwide, Financial Modeling Group, 131 Dartmouth St., Boston, MA 02116, USA)

  • Charlie Wusuo Liu

    (AIR-Worldwide, Financial Modeling Group, 131 Dartmouth St., Boston, MA 02116, USA)

  • Jayanta Guin

    (AIR-Worldwide, Financial Modeling Group, 131 Dartmouth St., Boston, MA 02116, USA)

Abstract

We present several fast algorithms for computing the distribution of a sum of spatially dependent, discrete random variables to aggregate catastrophe risk. The algorithms are based on direct and hierarchical copula trees. Computing speed comes from the fact that loss aggregation at branching nodes is based on combination of fast approximation to brute-force convolution, arithmetization (regriding) and linear complexity of the method for computing the distribution of comonotonic sum of risks. We discuss the impact of tree topology on the second-order moments and tail statistics of the resulting distribution of the total risk. We test the performance of the presented models by accumulating ground-up loss for 29,000 risks affected by hurricane peril.

Suggested Citation

  • Rafał Wójcik & Charlie Wusuo Liu & Jayanta Guin, 2019. "Direct and Hierarchical Models for Aggregating Spatially Dependent Catastrophe Risks," Risks, MDPI, vol. 7(2), pages 1-22, May.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:2:p:54-:d:229383
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    References listed on IDEAS

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    Cited by:

    1. Rafał Wójcik & Charlie Wusuo Liu, 2022. "Bivariate Copula Trees for Gross Loss Aggregation with Positively Dependent Risks," Risks, MDPI, vol. 10(8), pages 1-24, July.

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