Robust Estimation of Loss Models for Lognormal Insurance Payment Severity Data

TL;DR

This paper introduces robust estimation methods, including MLE and MTM, for lognormal insurance payment severity data affected by truncation, censoring, and scaling, with theoretical and simulation validation.

Contribution

It develops and compares new robust estimation procedures for lognormal severity models under various data transformations in insurance.

Findings

MLE and MTM estimators are derived and their asymptotic properties established.

Simulation studies demonstrate the estimators' performance and robustness.

Numerical examples illustrate practical application to US insurance data.

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.