The ultimate prediction uncertainty in the chain-ladder model of Mack: An unbiased estimator

2021 ◽  
Author(s):  
Filippo Siegenthaler
Keyword(s):  
Unbiased Estimator ◽  
Prediction Uncertainty ◽  
Ladder Model ◽  
Chain Ladder

scholarly journals Identification of the age-period-cohort model and the extended chain-ladder model

Biometrika ◽  
2008 ◽  
Vol 95 (4) ◽  
pp. 979-986 ◽  
Author(s):  
D. Kuang ◽  
B. Nielsen ◽  
J. P. Nielsen
Keyword(s):  
Cohort Model ◽  
Ladder Model ◽  
Extended Chain ◽  
Chain Ladder

scholarly journals Forecasting with the age-period-cohort model and the extended chain-ladder model

Biometrika ◽  
2008 ◽  
Vol 95 (4) ◽  
pp. 987-991 ◽  
Author(s):  
D. Kuang ◽  
B. Nielsen ◽  
J. P. Nielsen
Keyword(s):  
Cohort Model ◽  
Ladder Model ◽  
Extended Chain ◽  
Chain Ladder

scholarly journals Bayesian over-dispersed Poisson model and the Bornhuetter & Ferguson claims reserving method

2012 ◽  
Vol 6 (2) ◽  
pp. 258-283 ◽  
Author(s):  
Peter D. England ◽  
Richard J. Verrall ◽  
Mario V. Wüthrich
Keyword(s):  
Poisson Model ◽  
The Other ◽  
Prior Distributions ◽  
Prediction Uncertainty ◽  
General Insurance ◽  
Other Hand ◽  
Different Types ◽  
Chain Ladder ◽  
The One ◽  
Classical Chain

AbstractWe consider the Bayesian over-dispersed Poisson (ODP) model for claims reserving in general insurance. We choose two different types of prior distributions for the parameters and then study the different Bayesian predictors. This study leads, on the one hand, to the classical chain ladder predictor and, on the other hand, to Bornhuetter & Ferguson predictors. We highlight (either analytically or numerically) how these predictors are obtained and how their prediction uncertainty can be determined.

Chain ladder and maximum likelihood

1991 ◽  
Vol 118 (3) ◽  
pp. 489-499 ◽  
Author(s):  
R. J. Verrall
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Ladder Model ◽  
Second Moments ◽  
Chain Ladder

ABSTRACTThis paper derives second moments of estimates of the parameters in the chain ladder model. Thus, the so-called link ratios, and proportions of ultimate claims for each development year are considered. This enables confidence statements about the chain ladder parameters to be made with statistical rigour. The methods are illustrated using 6 sets of real data taken from the DTI returns.

scholarly journals Actuarial Evaluation of Late Losses: A Chain Ladder Model or a Generalized Linear Model of Rated Loss Increaments with a Poisson Distribution?

2020 ◽  
pp. 87-91
Author(s):  
Aleksey Vladimirovich Tanyukhin
Keyword(s):  
Linear Model ◽  
Poisson Distribution ◽  
Generalized Linear Model ◽  
Incremental Development ◽  
Ladder Model ◽  
Poisson Distributions ◽  
Chain Ladder ◽  
A Chain ◽  
Development Triangle

This article focuses on the equality of the estimated late losses resulting from the application of the chain ladder model to the estimates obtained on the basis of the incremental development triangle by cross-parameterizing the rated increments of losses with Poisson distributions using the generalized linear model. In this article, the formulas of the chain ladder model are derived by solving the problem of cross parameterization of rated increments of losses. Smaller accounting groups than the risk, along which the development triangle is formed, make conclusions about the possible bases for the sharing of reserves. This issue may be relevant for the further calculation of actuarial premiums.

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