Model Uncertainty and Selection of Risk Models for Left-Truncated and Right-Censored Loss Data

Qian Zhao, Sahadeb Upretee and Daoping Yu ()
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Qian Zhao: Department of Mathematics, Robert Morris University, Moon Township, PA 15108, USA
Sahadeb Upretee: Department of Mathematics, Central Washington University, Ellensburg, WA 98926, USA
Daoping Yu: Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA

Risks, 2023, vol. 11, issue 11, 1-17

Abstract: Insurance loss data are usually in the form of left-truncation and right-censoring due to deductibles and policy limits, respectively. This paper investigates the model uncertainty and selection procedure when various parametric models are constructed to accommodate such left-truncated and right-censored data. The joint asymptotic properties of the estimators have been established using the Delta method along with Maximum Likelihood Estimation when the model is specified. We conduct the simulation studies using Fisk, Lognormal, Lomax, Paralogistic, and Weibull distributions with various proportions of loss data below deductibles and above policy limits. A variety of graphic tools, hypothesis tests, and penalized likelihood criteria are employed to validate the models, and their performances on the model selection are evaluated through the probability of each parent distribution being correctly selected. The effectiveness of each tool on model selection is also illustrated using well-studied data that represent Wisconsin property losses in the United States from 2007 to 2010.

Keywords: left-truncation; right-censoring; model uncertainty; model selection; maximum likelihood estimation (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:11:y:2023:i:11:p:188-:d:1270522

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