Insurance practitioners rely on statistical models to predict future claims in order to provide financial protection. Proper predictive statistical modeling is more challenging when analyzing claims with lower frequency, but high costs. The paper investigated the use of predictive generalized linear models (GLMs) to address this challenge. Workers’ compensation claims with costs equal to or more than US$100,000 were analyzed in agribusiness industries in the Midwest of the USA from 2008 to 2016. Predictive GLMs were built with gamma, Weibull, and lognormal distributions using the lasso penalization method. Monte Carlo simulation models were developed to check the performance of predictive models in cost estimation. The results show that the GLM with gamma distribution has the highest predictivity power (R2 = 0.79). Injury characteristics and worker’s occupation were predictive of large claims’ occurrence and costs. The conclusions of this study are useful in modifying and estimating insurance pricing within high-risk agribusiness industries. The approach of this study can be used as a framework to forecast workers’ compensation claims amounts with rare, high-cost events in other industries. This work is useful for insurance practitioners concerned with statistical and predictive modeling in financial risk analysis.