What is the most appropriate model for estimating aggregate auto claims in a specific block of business?

The most appropriate model for estimating aggregate auto claims is a generalized linear model (GLM) with a Tweedie response. This choice is particularly suited for modeling aggregate claims because it can handle both the occurrence of events (claims) and the severity of those events (costs) simultaneously. The Tweedie distribution is a versatile family of distributions that includes the normal and gamma distributions and is particularly effective in scenarios where there are many zeros and positive continuous outcomes, such as insurance claims.

In the context of auto claims, the Tweedie model allows for the modeling of claim counts, including the possibility of no claims, as well as the magnitude of claims when they do occur. This is essential in insurance settings where a significant number of insureds may not file a claim. Additionally, the Tweedie model can capture over-dispersion—where the variance exceeds the mean—which is common in aggregate claim data.

While Poisson regression with exposures could be a contender, it typically assumes that the mean and variance of the claims are equal, which is not often the case in real-world data, especially in insurance contexts where high variability in claims is common. The negative binomial model helps address over-dispersion but primarily focuses on count data rather than