Counting models with excessive zeros ensuring stochastic monotonicity

TL;DR

This paper analyzes the limitations of standard count models with excessive zeros in insurance data, and proposes new models that ensure stochastic monotonicity for more consistent credibility adjustments.

Contribution

It introduces novel counting random-effect models that handle excessive zeros while maintaining stochastic monotonicity, addressing a key theoretical gap.

Findings

Standard models may violate stochastic monotonicity.

Proposed models ensure stochastic monotonicity and better credibility.

Models improve the theoretical consistency of insurance claim analysis.

Abstract

Standard count models such as the Poisson and Negative Binomial models often fail to capture the large proportion of zero claims commonly observed in insurance data. To address such issue of excessive zeros, zero-inflated and hurdle models introduce additional parameters that explicitly account for excess zeros, thereby improving the joint representation of zero and positive claim outcomes. These models have further been extended with random effects to accommodate longitudinal dependence and unobserved heterogeneity. However, their consistency with fundamental probabilistic principles in insurance, particularly stochastic monotonicity, has not been formally examined. This paper provides a rigorous analysis showing that standard counting random-effect models for excessive zeros may violate this property, leading to inconsistencies in posterior credibility. We then propose new classes of counting random-effect models that both accommodate excessive zeros and ensure stochastic monotonicity, thereby providing fair and theoretically coherent credibility adjustments as claim histories evolve.