SPLICE: a synthetic paid loss and incurred cost experience simulator

Abstract

Abstract In this paper, we first introduce a simulator of cases estimates of incurred losses called SPLICE (Synthetic Paid Loss and Incurred Cost Experience). In three modules, case estimates are simulated in continuous time, and a record is output for each individual claim. Revisions for the case estimates are also simulated as a sequence over the lifetime of the claim in a number of different situations. Furthermore, some dependencies in relation to case estimates of incurred losses are incorporated, particularly recognising certain properties of case estimates that are found in practice. For example, the magnitude of revisions depends on ultimate claim size, as does the distribution of the revisions over time. Some of these revisions occur in response to occurrence of claim payments, and so SPLICE requires input of simulated per-claim payment histories. The claim data can be summarised by accident and payment “periods” whose duration is an arbitrary choice (e.g. month, quarter, etc.) available to the user. SPLICE is built on an existing simulator of individual claim experience called SynthETIC (introduced in Avanzi et al. 2021b, Insurance: Mathematics and Economics, 100, 296–308), which offers flexible modelling of occurrence, notification, as well as the timing and magnitude of individual partial payments. This is in contrast with the incurred losses, which constitute the additional contribution of SPLICE. The inclusion of incurred loss estimates provides a facility that almost no other simulators do. SPLICE is is a fully documented R package that is publicly available and open source (on CRAN). SPLICE, combined with SynthETIC, provides 11 modules (occurrence, notification, etc.), any one or more of which may be re-designed according to the user’s requirements. It comes with a default version that is loosely calibrated to resemble a specific (but anonymous) Auto Bodily Injury portfolio, as well as data generation functionality that outputs alternative data sets under a range of hypothetical scenarios differing in complexity. The general structure is suitable for most lines of business, with some reparameterisation.