Benefits and premiums in life insurance contracts are typically paid contingent on the biometric state of the insured. Due to delays between the occurrence, reporting, and settlement of changes to the biometric state, the state process is not fully observable in real-time. This fact implies that the popular multi-state models for the biometric state of the insured are not able to describe the development of the policy in real-time.

When calculating prospective reserves, one therefore has to account for the fact that the currently observed biometric state might be changed retroactively due to the arrival of new information. This phenomenon gives rise to the need for incurred-but-not-reported (IBNR) and reported-but-not-settled (RBNS) models, which are currently not well described in the context of multi-state life-insurance models.

We highlight the need for a unifying approach. Subsequently, we give a fundamental treatment of the problem in the setting of continuous-time multi-state life insurance by introducing a new class of models: transaction time models. Furthermore, when specializing to disability insurance schemes, we derive an explicit formula for the IBNR and RBNS reserves.

Find the Q&A here: Q&A on 'Mortality Models from Different Perspectives'