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 and 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.
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