A stochastic method for claims reserving in general insurance

Abstract

The paper addresses the problem of estimating future claim payments from the 'run-off' of past claim payments. A model of the claim payment process is postulated. Results from risk theory are applied to give a model for the incremental paid claims data by development period. A fitting method is developed which takes account of the error structure of the data implied by the underlying model of the claim payment process. The application of a similar method to incremental incurred data is considered. A numerical example is given.

State Space Models and the Kalman-Filter in Stochastic Claims Reserving: Forecasting, Filtering and Smoothing

“…In the first category, the authors De Jong and Zehnwirth (1983), Wright (1990), Zehnwirth (1997), Taylor et al (2003) and Pang and He (2012) mainly use variations on the Hoerl curve to model the claims data over the development years. The general exponential-logarithmic Hoerl curve is given as β j = exp(κj + δ log j) with development year parameter β j for all j = 0, .…”

A generalized linear model with smoothing effects for claims reserving

“…England & Verrall (2001) for the derivation. The term u ij is a known offset, a function of an exposure and a known adjustment term, see Wright (1990), while δk allows for claims inflation. It is easy to see that (2.11) is similar to the Hoerl curve in (2.8), but the relation between the responses and the predictor differs.…”

“…Moreover, the error distribution no longer has to be normal. Wright (1990) used the Kalman filter to produce smoothed estimates of the parameters. Renshaw & Verrall (1998) used (2.7) in (2.10) and related the model to the chain-ladder method for p = 1.…”

Claims Reserving Using Tweedie's Compound Poisson Model

“…It is then straightforward to use generalized linear model (GLM) methods for parameter estimations. A significant first step into that direction has been done by Wright [11].…”