Estimation of Tail Development Factors in the Paid-Incurred Chain Reserving Method

In many applied claims reserving problems in P&C insurance, the claims settlement process goes beyond the latest development period available in the observed claims development triangle. This makes it necessary to estimate so-called tail development factors which account for the unobserved part of the insurance claims. We estimate these tail development factors in a mathematically consistent way. This paper is a modification of the paid-incurred chain (PIC) reserving model of Merz and Wüthrich (2010). This modification then allows for the prediction of the outstanding loss liabilities and the corresponding prediction uncertainty under the inclusion of tail development factors.