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Estimation of Outstanding Claims Liability Using Empirical Moments of Correlated Random Sum

Aceng Komarudin Mutaqin, Sutawanir Darwis, Dumaria Rulina Tampubolon, Rianto Ahmadi Djojosugito


The estimation of outstanding claims liability (OCL) is one of the important issues in the long-tail insurance business. OCL is related to the future payments for claims which have been incurred but are not yet settled. There are two common approaches to estimate OCL. The first approach is based on the aggregate claim payments data in form of a run-off triangle, and the second approach is based on the individual claim payments data. Many different statistical methods are available for both approaches. In this paper we discuss a new alternative method to estimate OCL for claims which have been reported but are not yet settled. The estimation is based on the individual claim payment data using the empirical moments of correlated random sum. Our method assumes that the total payments amount for a claim is a correlated random sum. Simulations are conducted to compare the performance of our method and chain ladder method commonly used as a gold standard to estimate OCL. The simulation results show that for almost all cases, particularly for a few total number of claims, our method has better performance than the chain ladder method, and our method with including covariate has better performance than without including covariate.


long-tail insurance business; outstanding claims liability; chain ladder method; empirical moment; correlated random sum; Monte Carlo simulation.

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