Bridging the gap between pricing and reserving with an occurrence and development model for non-life insurance claims

Abstract

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 one step approach suitable 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 allows to resolve the inconsistency in traditional pricing techniques between actual, complete observations on the one hand and best estimates on the other hand. We illustrate our proposed model on a reinsurance portfolio, where large uncertainties in the best estimates originate from long reporting and settlement delays, low claim frequencies and heavy (even extreme) claim sizes.

Measuring Variable Importance in Generalized Linear Models for Modeling Size of Loss Distributions

“…One may need to see that, among all factors considered in the model, what the measures in terms of their importance to model buildings are, mainly when factors are categorical and consist of many different factor levels. Therefore, the investigation of suitable approaches to measuring variable importance in insurance pricing has become an emerging research area and has attracted significant attention in machine learning for insurance [11,[17][18][19].…”