Economics - Research Publications

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Type: Preprint × Start date: 2000 × End date: 2009 × Subject: chain ladder × Author: TAYLOR, GREGORY ×

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    Loss reserving with GLMs : a case study
    Taylor, Greg ; McGuire, Gráinne ( 2004-05)
    This paper provides a case study in the application of generalised linearmodels (“GLMs”) to loss reserving. The study is motivated by approachingthe exercise from the viewpoint of an actuary with a predisposition to theapplication of the chain ladder (“CL”).The data set under study is seen to violate the conditions for application of theCL in a number of ways. The difficulties of adjusting the CL to allow forthese features of the data are noted (Sections 3).Regression, and particularly GLM regression, is introduced as a structured andrigorous form of data analysis. This enables the investigation and modellingof a number of complex features of the data responsible for the violation of the CL conditions. These include superimposed inflation and changes in the rules governing the payment of claims (Sections 4 to 7).The development of the analysis is traced in some detail, as is the production of a range of diagnostics and tests used to compare candidate models and validate the final one.The benefits of this approach are discussed in Section 8.
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    Further Observations on Chain Ladder Bias
    Taylor, Greg ( 2002-01)
    The chain ladder forecast (CLF) has previously been shown to be biased upward. The present paper calculates the second order approximation to the magnitude of the bias, ie the Taylor series for the bias truncated at terms involving second order moments of observations. Some order relations between data triangles are obtained with respect to this second order bias. While the prediction error of the CLF, as a predictor of loss reserve, does not have zero mean, it does have zero median under certain circumstances. Some numerical consequences are explored.
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    Chain Ladder Bias
    Taylor, Greg ( 2002-01)
    The chain ladder forecast of oustanding losses is known to be unbiased under suitable assumptions. According to these assumptions, claim payments in any cell of a payment triangle are dependent on those from preceding development years of the same accident year. If all cells are assumed stochastically independent, the forecast is no longer unbiased. Section 6 shows that, under very general assumptions, it is biased upward. This result is linked to earlier work on some stochastic versions of the chain ladder.