Bivariate Copula Trees for Gross Loss Aggregation with Positively Dependent Risks

Rafał Wójcik and Charlie Wusuo Liu
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Rafał Wójcik: Verisk Extreme Event Solutions, Financial Modeling Group, Lafayette City Center, 2 Avenue de Lafayette, 2nd Floor, Boston, MA 02111, USA
Charlie Wusuo Liu: Verisk Extreme Event Solutions, Financial Modeling Group, Lafayette City Center, 2 Avenue de Lafayette, 2nd Floor, Boston, MA 02111, USA

Risks, 2022, vol. 10, issue 8, 1-24

Abstract: We propose several numerical algorithms to compute the distribution of gross loss in a positively dependent catastrophe insurance portfolio. Hierarchical risk aggregation is performed using bivariate copula trees. Six common parametric copula families are studied. At every branching node, the distribution of a sum of risks is obtained by discrete copula convolution. This approach is compared to approximation by a weighted average of independent and comonotonic distributions. The weight is a measure of positive dependence through variance of the aggregate risk. During gross loss accumulation, the marginals are distorted by application of insurance financial terms, and the value of the mixing weight is impacted. To accelerate computations, we capture this effect using the ratio of standard deviations of pre-term and post-term risks, followed by covariance scaling. We test the performance of our algorithms using three examples of complex insurance portfolios subject to hurricane and earthquake catastrophes.

Keywords: gross loss; catastrophe insurance; copula-based risk aggregation; dependence; correlation; tail risk; financial terms; copula convolution; aggregate distribution; stop-loss order; comonotonic risk (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2022
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