Forecasting the Pricing Kernel of IBNR Claims Development in Property-Casualty Insurance

Abstract

A new method of forecasting the pricing kernel, i.e., stochastic claim inflation or link ratio function, of incurred but not reported (IBNR) claims (in property-casualty insurance) from residuals in a dynamic claims forecast model is presented. We employ a pseudo Kalman filter approach by using claims risk exposure estimates to reconstruct innovations in stochastic claims development. Whereupon we find that the pricing kernel forecast is a product measure of the innovations. We show how these results impact performance measurement including but not limited to risk-adjusted return on capital by and through insurance accounting relationships for adjusted underwriting results; and loss ratio or pure premium calculations. Additionally, we show how, in the context of Wold decomposition, diagnostics from our model can be used to compute signal to noise ratio for, and cross check, unobservable pricing kernels used to forecast claims. Furthermore, we prove that a single risk exposure factor connects seemingly unrelated specifications for loss link ratio, and claims volatility.

Keywords: IBNR claims ladder, claims reserve forecast, stochastic claim inflation, claims risk exposure, link ratio function, property-casualty insurance, insurance accounting

JEL Classification: C53, G22, G28, M49