"Cash Flow and Unpaid Claim Runoff Estimates Using Mack and Merz-Wüthrich Models"

"Cash Flow and Unpaid Claim Runoff Estimates Using Mack and Merz-Wüthrich Models"

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For both Solvency II and IFRS 17 the actuary can use unpaid claim variability estimates for cash flows and the runoff of unpaid claims in addition to the more widely used accident year view of the unpaid claims. This paper is based on a review of the foundational Mack and Merz-Wüthrich formulas and their decomposition into process variance and parameter uncertainty, per future diagonal. The decompositions are then used to show how modifications to the accident year formulas can be used to calculate the standard deviations for cash flow and unpaid claim runoff estimates. The paper will demonstrate that while the Merz-Wüthrich formulas (and by extension the England, Verrall & Wüthrich formulas) are an elegant bridge between the 1-year time horizon and the ultimate time horizon used by Mack, there is an alternative formulation for the runoff of the N-year time horizon that better fits the Solvency II environment.

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