Loss Emergence: Predicting IBNYR & INFRA Delays, Events and Costs

An IBNR event is one that occurs at a random rate during some fixed exposure interval and incurs a random delay before it is reported. In practical cases, neither the Poisson intensity parameter nor the parameters of the delay distribution are known precisely. Previous research has shown how to use the number of reported events in some longer interval to estimate the joint density of these parameters and to predict the density of the number of IBNYR (Incurred But Not Yet Reported) events, using Bayesian analysis upon the underlying random occurrence/random delay model. Specific examples were given for reporting and predicting one exposure year’s events in continuous and discrete time, as well as the usual IBNR Triangle multiple exposure year, discrete-time format. We begin with a survey of these results, stressing the formulation of the model, the assumptions required, the numerical approximations needed, as well as the advantages of producing full predictive distributions, rather than point estimates. When we consider the costs associated with these events, we introduce not only uncertain parameters in the underlying severity distributions, but also the possibility of statistical dependence between costs and event generation and delays. Thus additional modeling assumptions are needed to predict both claim severities attached to IBNYR events, as well as to the IBNFR (Incurred But Not Fully Reported) claims. For the IBNYR events, and independence between the unknown random parameters, our previous methods generalize in straightforward way, using both reported events and severities. However, prediction of the undeveloped costs of IBNFR events will require a great deal of practical investigation and modeling before we can predict total IBNR losses with any confidence.