Pricing Milk Index Insurance Under a Hybrid Mean‐Splitting and Neural Framework

Milk production in Malawi remains highly vulnerable to climate variability and feed uncertainty, creating substantial income risk for dairy farmers. This study develops a rainfall‐ and temperature‐driven feed quality index and integrates it into an index‐based insurance pricing framework using a hybrid mean‐splitting decomposition (MSD), Bayesian neural network (BNN), and long short‐term memory (LSTM) approach. Temperature and rainfall are modeled through a Fokker–Planck equation process to construct a latent variable that preserves their interdependence. The feed quality index is decomposed into components that capture temporal trends and seasonal effects driven by weather variables. Empirical results based on daily data (2022–2025) show that Holstein cattle exhibit the highest average milk yield (131.7 L), compared to Friesian (87.2 L) and Jersey (82.5 L). The hybrid MSD–BNN–LSTM framework demonstrates strong predictive performance, with out‐of‐sample R ² values ranging from approximately 0.69 to 0.74 for the seasonal component and from 0.91 to 0.93 for the trend component, indicating better out‐of‐sample predictive performance within the 2022–2025 observation period. The reconstructed feed quality index maintains acceptable predictive accuracy, with R ² values above 60%. The proposed insurance pricing framework shows that premiums increase with loss thresholds while maintaining stable loss probabilities, thereby reducing basis risk. Holstein premiums increase from USD 1.22 at 25% loss to USD 6.50 at 35% loss, while Jersey premiums rise from USD 2.22 to USD 8.50 over the same range. Friesian cattle exhibit relatively stable premiums, reflecting greater resilience to local conditions.