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Robust estimation of loss models for lognormal insurance payment severity data. (English) Zbl 1479.91339

The authors propose two estimation procedures – maximum likelihood estimator (MLE) and method of trimmed moments (MTM) – for the mean and variance of lognormal insurance payment severity data sets affected by different loss control mechanisms in the financial and insurance industries. Examples of such loss control mechanism are: truncation (due to deductibles), censoring (due to policy limits), and scaling (due to coinsurance proportions). Maximum likelihood estimating equations for both payment-per-payment and payment-per-loss data sets are derived which can be solved by existing iterative numerical methods. The asymptotic distributions of those estimators are established via Fisher information matrices. A dynamic MTM estimation procedures is developed for lognormal claim severity models for the transformed data scenarios. Numerical examples for 1500 US indemnity losses are provided which illustrate the practical performance of the established results.

MSC:

91G05 Actuarial mathematics
62P05 Applications of statistics to actuarial sciences and financial mathematics
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