The Chain Ladder and Tweedie Distributed Claims Data

By Greg Taylor

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Abstract

The paper considers a model with multiplicative accident period and development period effects, and derives the ML equations for parameter estimation in the case that the distribution of each cell of the claims triangle is a general member of the Tweedie family.

This yields someknown special cases, e.g., over-dispersed Poisson (ODP) distribution (Tweedie parameter p = 1), for which the chain ladder algorithm is known to provide maximum likelihood (ML) parameter estimates, and gamma distribution (p = 2). The intermediate cases (1 < p < 2) represent compound Poisson cell distributions with gamma severity distributions.

While ML estimates are not chain ladder for Tweedie distributions other than ODP, the paper investigates why they will be close to chain ladder under certain circumstances. It is also demonstrated that the ML estimates for the general Tweedie case can be obtained by application of the chain ladder algorithm to transformed data. This is illustrated numerically.

KEYWORDS: Chain ladder, maximum likelihood, separation method, Tweedie distribution

Citation

Taylor, Greg, "The Chain Ladder and Tweedie Distributed Claims Data," Variance 3:1, 2009, pp. 96-104.

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Variance is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.