  Due to the presence of reporting and settlement delay, claim data sets
collected by non-life insurance companies are typically incomplete, facing
right censored claim count and claim severity observations. Current practice in
non-life insurance pricing tackles these right censored data via a two-step
procedure. First, best estimates are computed for the number of claims that
occurred in past exposure periods and the ultimate claim severities, using the
incomplete, historical claim data. Second, pricing actuaries build predictive
models to estimate technical, pure premiums for new contracts by treating these
best estimates as actual observed outcomes, hereby neglecting their inherent
uncertainty. We propose an alternative approach that brings valuable insights
for both non-life pricing as well as reserving. As such we effectively bridge
these two key actuarial tasks that have traditionally been discussed in silos.
Hereto we develop a granular occurrence and development model for non-life
claims that tackles reserving and at the same time resolves the inconsistency
in traditional pricing techniques between actual observations and imputed best
estimates. We illustrate our proposed model on an insurance as well as a
reinsurance portfolio. The advantages of our proposed strategy are most
compelling in the reinsurance illustration where large uncertainties in the
best estimates originate from long reporting and settlement delays, low claim
frequencies and heavy (even extreme) claim sizes.
