Nested Copula Reserving for Claims in General Insurance

Date

2026-2-10

Author

Koçer, Günay Burak

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Regulatory frameworks such as Solvency II and IFRS 17 require credible identification of reserve uncertainty and tail risk, which encourages models that move beyond deterministic Chain-Ladder approaches. This study proposes a reserving framework that uses quarterly paid claims triangles obtained from a non-life insurance company operating in Türkiye to estimate high-dimensional D-vine copulas through successively selected pairwise copula families that consider dependency throughout development periods. To encompass portfolio-level risk, the framework is extended through a nested copula structure: inner D-vines model temporal dependencies within each line, while an outer R-vine aims to capture inter-line correlations. This hierarchical approach maintains superior point estimation accuracy compared to the Chain-Ladder method, allows for a realistic diversification assessment, and delivers significantly lower tail risk estimates based on independence assumptions. The proposed framework provides appropriate reserve allocations for regulatory capital calculation and risk adjustment, and effectively captures dependency structures through comprehensive uncertainty quantification.

Subject Keywords

Claims Reserving, Chain Ladder, Nested Copula, Conditional Vine Copula, D-vine, R-vine

URI

https://hdl.handle.net/11511/118419

Collections

Graduate School of Applied Mathematics, Thesis