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

Abstract

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 $\frac{1}{ϕ_i}$, where $ϕ_i$ 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 $250\times$ faster than the approximation-based benchmark, establishing it as the only computationally and statistically valid approach for heterogeneous producer pools.