A Continuous Version of Sherman’s Inverse Power Curve Model with Simple Cumulative Development Factor Formulas

A continuous version of Sherman’s discrete inverse power curve model for loss development is defined. This continuous version, apparently unlike its discrete counterpart, has simple formulas for cumulative development factors, including tail factors. The continuous version has the same tail convergence conditions and basic analytical properties as the discrete version. Parameter fitting and numerical comparisons between the discrete and continuous model versions are explored.