Professor Dr. Alois Gisler: The Reserve Risk of the Chain-Ladder Reserving Method from a New Perspective
Prof. Dr. Alois Gisler (ETH Zurich, RiskLab Switzerland) holds a seminar with the title "The Reserve Risk of the Chain-Ladder Reserving Method from a New Perspective"
Chain ladder (CL) is still one of the most popular and most used reserving method in the insurance practice. In 1993 Mack derived a formula for the uncertainty of the CL-reserves. Mack's formula refers to the ultimate run-off uncertainty. For solvency one has to quantify the one-year run-off uncertainty. In 2008 Merz and Wüthrich derived such a formula, which is probably the most used formula for estimating the reserve risk for solvency purposes. There are further requirements from solvency II: to estimate the risk margin one also needs estimators for the one-year run-off risk in future accounting years. In a recent paper of end 2014, Merz and Wüthrich have also derived formulas for these risks. All these formulas were derived by different techniques with increasing sophistication from Mack to the most recent paper by Merz and Wüthrich.
In the talk we derive the same results by a unified approach. To be more precise, the formulae received look different, but yield the same results. The main idea is to start with a first order Taylor approximation. The advantages of this alternative derivation and of this new perspective are:
a) the derivations of the results are much simpler, shorter and can easily be understood by practitioners,
b) the formulae for the total over all accident years are much simpler,
c) the formulae become intuitively accessible.