Parameter reduction in log-normal chain-ladder models
type: Item
instance of: scholarly article
title: Parameter reduction in log-normal chain-ladder models
zbMATH Open document ID: 1403.91202
author: Mario V. Wüthrich
author: Richard Verrall
published in: European Actuarial Journal
publication date: 2016-01-15T00:00:00Z
full work available at URL: Parameter Reduction in LogNormal CL Models.pdf
review text: The chain-ladder method is one of the most popular methods to calculate the reserves in actuarial sciences. A special model is considered, where the claim development factors \(C_{i,j}\) are modelled as \[ C_{i,j} = C_{i,j-1} (\exp\{\xi_{i,j}\} + 1)\,. \] Here \(C_{i,j}\) are the aggregate payments for claims with occurrence year \(i\) paid until year \(i+j\). Given the parameters \(\Theta = (\theta_0, \theta_1, \ldots, \theta_J)\) for the occurrence years \(0,1,\ldots,J\), it is assumed that \((\xi_{i,j})\) are independent normally distributed. The variances are fixed, but the mean values \(\theta_i\) are normally distributed. For a fixed \(k\), in the model \(M^{(k)}\) the parameters \(\theta_j: 0 \leq j \leq k\) are independent, but \(\theta_j = \alpha - j \beta\) for \(j > k\), where \(\alpha,\beta\) are independent normal variables. For the model \(M^{(k)}\), Bayesian statistics can be done to predict the necessary reserves. If one does not want to make the normal assumption for the unknown parameters, an empirical Bayes approach would lead to a simple way to update the reserves if more observations are known. In order to keep the model as simple as necessary, Akaike's information criterion can be used to choose the model. Because the parameters \(\theta_k\) are random, the model risk can be included in the calculation of the reserves. An insurance example illustrates the method.
reviewed by: Hanspeter Schmidli
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 62F15
Mathematics Subject Classification ID: 62C10
Mathematics Subject Classification ID: 62C12
zbMATH DE Number: 6530525
zbMATH Keywords: chain-ladder
zbMATH Keywords: lognormal model
zbMATH Keywords: Bayesian inference
zbMATH Keywords: empirical Bayes approach
zbMATH Keywords: Akaike's information criterion
MaRDI profile type: Publication
OpenAlex ID: W1172920345
cites work: A new look at the statistical model identification
cites work: A course in credibility theory and its applications
cites work: Prediction error for credible claims reserves: an \(h\)-likelihood approach
cites work: Q3994345
cites work: Q4715592
cites work: Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect models and structured dispersions
cites work: A Bayesian Log-Normal Model for Multivariate Loss Reserving
cites work: Claims reserving and generalised additive models
cites work: Reversible Jump Markov Chain Monte Carlo Method for Parameter Reduction in Claims Reserving
cites work: “A Bayesian Log-Normal Model for Multivariate Loss Reserving”, Peng Shi, Sanjib Basu, and Glenn G. Meyers, March 2012
cites work: Stochastic claims reserving methods in insurance
DOI: 10.1007/S13385-015-0114-7
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description: scientific article; zbMATH DE number 6530525