Delta Boosting Implementation of Negative Binomial Regression in Actuarial Pricing

Abstract

This study proposes an efficacious approach to analyze the over-dispersed insurance frequency data as it is imperative for the insurers to have decisive informative insights for precisely underwriting and pricing insurance products, retaining existing customer base and gaining an edge in the highly competitive retail insurance market. The delta boosting implementation of the negative binomial regression, both by one-parameter estimation and a novel two-parameter estimation, was tested on the empirical data. Accurate parameter estimation of the negative binomial regression is complicated with considerations of incomplete insurance exposures, negative convexity, and co-linearity. The issues mainly originate from the unique nature of insurance operations and the adoption of distribution outside the exponential family. We studied how the issues could significantly impact the quality of estimation. In addition to a novel approach to simultaneously estimate two parameters in regression through boosting, we further enrich the study by proposing an alteration of the base algorithm to address the problems. The algorithm was able to withstand the competition against popular regression methodologies in a real-life dataset. Common diagnostics were applied to compare the performance of the relevant candidates, leading to our conclusion to move from light-tail Poisson to negative binomial for over-dispersed data, from generalized linear model (GLM) to boosting for non-linear and interaction patterns, from one-parameter to two-parameter estimation to reflect more closely the reality.