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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Zhao, Qian, Upretee, Sahadeb, Yu, Daoping
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911768297603072
author Zhao, Qian
Upretee, Sahadeb
Yu, Daoping
author_facet Zhao, Qian
Upretee, Sahadeb
Yu, Daoping
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2401_17518
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Model Uncertainty and Selection of Risk Models for Left-Truncated and Right-Censored Loss Data
Zhao, Qian
Upretee, Sahadeb
Yu, Daoping
Methodology
Statistics Theory
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.
title Model Uncertainty and Selection of Risk Models for Left-Truncated and Right-Censored Loss Data
topic Methodology
Statistics Theory
url https://arxiv.org/abs/2401.17518