A Least Squares Estimation of a Hybrid log-Poisson Regression and its Goodness of Fit for Optimal Loss Reserves in Insurance

TL;DR

This paper introduces a hybrid log-Poisson regression model estimated via fuzzy least-squares, along with a goodness-of-fit measure, to improve loss reserving accuracy in insurance compared to classical methods.

Contribution

It proposes a novel hybrid log-linear model estimated with fuzzy least-squares and develops a goodness-of-fit measure for better loss reserving assessment.

Findings

The hybrid model performs well on real loss reserving data.

The goodness-of-fit measure effectively compares the hybrid and classical models.

Results indicate improved accuracy over traditional log-Poisson regression.

Abstract

In this article, the parameters of a hybrid log-linear model (log-Poisson) are estimated using the fuzzy least-squares (FLS) procedures (Celmi\c{n}\v{s}, 987a,b, D'Urso and Gastaldi, 2000, DUrso and Gastaldi, 2001). A goodness of fit have been derived in order to assess and compare this new model and the classical log-Poisson regression in loss reserving framework (Mack, 1991). Both the hybrid model and its goodness of fit are performed on a loss reserving data.