Due to the presence of reporting and settlement delay, historical claim data sets in non-life insurance are typically incomplete. As a result observed claim counts and claim severities are right censored. Therefore, non-life insurance pricing is currently approached via a two-step procedure. First, insurers compute best estimates for claim frequency and severity at the level of individual policies based on the incomplete, historical claim data. Second, pricing actuaries build predictive models to estimate technical, pure premiums for new policies by treating these best estimates as actual observed outcomes, hereby neglecting the uncertainty present in them. We propose an alternative one-step approach for non-life pricing by analysing the incomplete information registered during the development of claims. The granularity of our model allows it to be applied to both pricing and reserving, hence bridging two key actuarial tasks that have traditionally been discussed in silos. We illustrate our proposed model on a reinsurance portfolio, where large uncertainties in the best estimates result from long reporting and settlement delays, low claim frequencies and extreme claim sizes.