One-Year and Total Run-Off Reserve Risk Estimators Based on Historical Ultimate Estimates

By Filippo Siegenthaler

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This paper presents closed-form formulas in order to estimate, based on the historical triangle of ultimate estimates, both the one-year and the total run-off reserve risk. This is helpful in case (as is often usual in practice) the reserve risk formulas related to the applied reserving methodology are unknown or in case such formulas cannot be rigorously derived since a fully well-defined stochastic model supporting the reserving methodology is missing (e.g., due to mixing of reserving methods).

Keywords: Reserve risk, mean square error of prediction, one-year prediction uncertainty, total run-off prediction uncertainty, ultimate estimates


Siegenthaler, Filippo, "One-Year and Total Run-Off Reserve Risk Estimators Based on Historical Ultimate Estimates," Variance 12:2, 2019, pp. 249-277.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.