Approximating the Bias and Variance of Chain Ladder Estimates Under a Compound Poisson Model

We consider the problem of estimating the outstanding claims produced by a homogeneous general insurance portfolio. The specific model considered in this paper is one where the number of claims in any loss period follows a Poisson distribution, settlement delays follow the same multinomial distribution, and settlements are single lump sums that are independent identically distributed random variables. Simulations using this model reveal that the development ratios and the outstanding claims estimates produced using the chain ladder method are positively biased. We obtain approximate formulas for the biases using Taylor series expansions of the random variables about their means. The same methods are used to obtain approximations for the variances and covariances of the projection ratios and the outstanding claims estimates. A simulation study reveals that our formulas are highly accurate