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ROBUST ESTIMATION OF LOSS MODELS FOR LOGNORMAL INSURANCE PAYMENT SEVERITY DATA

Published online by Cambridge University Press:  05 March 2021

Chudamani Poudyal Open the ORCID record for Chudamani Poudyal [Opens in a new window]
Chudamani Poudyal*
Affiliation:
Department of Mathematics, Tennessee Technological University, Cookeville, TN38505, USA E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

The primary objective of this scholarly work is to develop 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 mechanism, for example, truncation (due to deductibles), censoring (due to policy limits), and scaling (due to coinsurance proportions), in insurance and financial industries. Maximum likelihood estimating equations for both payment-per-payment and payment-per-loss data sets are derived which can be solved readily by any existing iterative numerical methods. The asymptotic distributions of those estimators are established via Fisher information matrices. Further, with a goal of balancing efficiency and robustness and to remove point masses at certain data points, we develop a dynamic MTM estimation procedures for lognormal claim severity models for the above-mentioned transformed data scenarios. The asymptotic distributional properties and the comparison with the corresponding MLEs of those MTM estimators are established along with extensive simulation studies. Purely for illustrative purpose, numerical examples for 1500 US indemnity losses are provided which illustrate the practical performance of the established results in this paper.

Keywords

Dynamic estimationlognormal insurance severitymaximum likelihood estimatorstrimmed momentsinsurance paymentsloss modelsrobust estimationtruncated and censored data
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 2 , May 2021 , pp. 475 - 507
Copyright
© 2021 by Astin Bulletin. All rights reserved

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