Federated Learning for the Design of Parametric Insurance Indices under Heterogeneous Renewable Production Losses

We propose a federated learning framework for the calibration of parametric insurance indices under heterogeneous renewable energy production losses. Producers locally model their losses using Tweedie generalized linear models and private data, while a common index is learned through federated optimization without sharing raw observations. The approach accommodates heterogeneity in variance and link functions and directly minimizes a global deviance objective in a distributed setting. We establish theoretical guarantees under sub-exponential covariate distributions, showing that the Lipschitz constants of the local Tweedie objectives scale as frac1φi, where φi is the dispersion parameter of producer i. This heterogeneity in smoothness causes naive federated averaging to be biased toward producers with stable microclimates --- precisely those least in need of basis-risk protection --- and motivates the use of corrected aggregation schemes. We implement and compare FedAvg, FedProx and FedOpt, and benchmark them against an existing approximation-based aggregation method. A progressive pool expansion experiment involving up to 121 solar farms in Germany reveals that the approximation-based method becomes entirely non-computable beyond the pool of 50 farms, while federated learning remains valid and actively improves as the pool grows. Federated learning is also over 250× faster than the approximation-based benchmark, establishing it as the only computationally and statistically valid approach for heterogeneous producer pools.