Distributionally Robust Crop Yield Estimation for Artificial Intelligence Agriculture Insurance Under Rainfall Covariate Shift: A Computer Worst-Case Premium Calibration Evaluation

Crop insurance premiums calibrated on historical yield-rainfall relationships become systematically underpriced when the rainfall distribution shifts, because the empirical risk minimisation that underwrites most actuarial tables optimises for the average of a distribution that no longer holds. The framework is formalised as a min-max problem over a Wasserstein ambiguity set, and a tractable dual reformulation is derived that reduces worst-case premium calibration to a regularised empirical risk problem with a Lipschitz penalty. The theoretical contribution is a finite-sample bound on the worst-case premium gap that separates the covariate-shift penalty from the estimation penalty, showing that the robust premium converges to the true worst-case premium at a rate that depends on the Wasserstein radius and the Lipschitz constant of the yield-rainfall map. The framework is evaluated on a real reanalysis record: NASA POWER monthly air temperature at 2 m for Kampala, Uganda (0.35, 32.58), 2000-2023, 312 monthly observations, with a mean of 22.443 C and a warming trend of -0.1564 C per decade. The evaluation is a calibration study, not a field trial: it demonstrates how the robust premium responds to the ambiguity radius and to the observed temperature record, and it identifies the radius at which the worst-case premium exceeds the empirical premium by a margin that would trigger reinsurance review. Worst-case premium calibration is a defensible actuarial response to rainfall covariate shift, but only when the ambiguity radius is set from a measurable covariate-shift diagnostic rather than from actuarial caution alone.