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

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. Under Solvency II, the concept of the one-year time horizon adds a new dimension to the estimates for unpaid claim distributions. This paper focuses on the closed form model developed by Mack, modified by Merz & Wüthrich to address the one-year horizon under Solvency II, and on its extension for two-year, three-year, etc. time windows that can be reconciled back to the original Mack formulas.