Direct and Hierarchical Models for Aggregating Spatially Dependent Catastrophe Risks

Rafał Wójcik, Charlie Wusuo Liu and Jayanta Guin
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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

Risks, 2019, vol. 7, issue 2, 1-22

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.

Keywords: risk aggregation; numerical convolution; copula trees; Monte-Carlo simulation; spatial correlation (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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