The Linear Markov Property in Credibility Theory

Abstract

We study the linear Markov property, i.e. the possibility of basing the credibility estimator on data of the most recent time period without loss of accuracy. Necessary and sufficient conditions are derived generally. The meaning of the linear Markov property is also discussed in different experience rating and loss reserving models.

IBNR models with random delay distributions

“…Kid-in which case we have Illl}d = 1 'if h,}, d. One should also note that the linear predictor of Sid should be based only the claim numbers, if available, when the model prescribes that 'P j is nonrandom, because in that model the Kid will be linear sufficient, see Witting (1987 Two models with random delay distributions are presented in this section. The first model generalises slightly the approach of Hesselager & Witting (1988), who assume that the delay probabilities follow a Dirichlet distribution, and through that assumption are able to derive a matrix-free expression for the credibility predictor.…”