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

TL;DR

This work addresses basis risk in parametric insurance for heterogeneous renewable production by introducing a horizontal federated learning framework to calibrate a common weather index Z = a^T Y. Each producer uses a producer-specific Tweedie GLM with latent parameters p_i, q_i, and φ_i, while a shared index is learned in a distributed, privacy-preserving manner via FL algorithms (FedAvg, FedProx, FedOpt). The global objective minimizes the Tweedie deviance across producers, enabling robust index design without centralizing data, and is benchmarked against an approximation-based ANOR method. Empirical results on a 50-plant solar dataset from Germany show that FL can recover index coefficients close to ANOR under moderate heterogeneity, while offering a more general, scalable framework and clear regulatory advantages. The study demonstrates FL’s relevance for actuarial practice, providing a principled path toward privacy-preserving, collaborative parametric insurance design in climate-sensitive energy portfolios.

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 implement and compare FedAvg, FedProx and FedOpt, and benchmark them against an existing approximation-based aggregation method. An empirical application to solar power production in Germany shows that federated learning recovers comparable index coefficients under moderate heterogeneity, while providing a more general and scalable framework.

Figures (7)

• Figure 1: Monte Carlo mean and confidence intervals of the global Tweedie deviance across communication rounds for FedAvg, FedProx, and FedOpt.
• Figure 2: Monte Carlo mean and confidence intervals of coefficient $a_1$ across federated learning algorithms.
• Figure 3: Monte Carlo mean and confidence intervals of coefficient $a_2$ across federated learning algorithms.
• Figure 4: Evolution of basis risk for park "Oberrammersdorf"
• Figure 5: Evolution of basis risk for park "Hilpoltstein"