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One-year and ultimate correlations in dependent claims run-off triangles

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  • Delong, Łukasz
  • Szatkowski, Marcin

Abstract

We investigate bottom-up risk aggregation applied by insurance companies facing reserve risk from multiple lines of business. Since risk capitals should be calculated in different time horizons and calendar years, depending on the regulatory or reporting regime (Solvency II vs IFRS 17), we study correlations of ultimate losses and correlations of one-year losses in future calendar years in lines of business. We consider a multivariate version of a Hertig’s lognormal model and we derive analytical formulas for the ultimate correlation and the one-year correlations in future calendar years. Our main conclusion is that the correlation coefficients that should be used in a bottom-up aggregation formula depend on the time horizon and the future calendar year where the risk emerges. We investigate analytically and numerically properties of the ultimate and the one-year correlations, their possible values observed in practice, and the impact of misspecified correlations on the diversified risk capital.

Suggested Citation

  • Delong, Łukasz & Szatkowski, Marcin, 2025. "One-year and ultimate correlations in dependent claims run-off triangles," Annals of Actuarial Science, Cambridge University Press, vol. 19(1), pages 159-192, March.
    • Handle: RePEc:cup:anacsi:v:19:y:2025:i:1:p:159-192_8
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