Neural network-based index insurance and optimal reinsurance strategies

Abstract

This thesis addresses two critical challenges in modern insurance risk management through the development of innovative mathematical frameworks that balance theoretical rigor with practical implementation. The research contributes to both agricultural risk transfer mechanisms and reinsurance optimization strategies, providing solutions that accommodate multiple stakeholder perspectives while maintaining computational tractability.

The first study develops a neural network-based framework for weather index insurance design that addresses fundamental challenges in agricultural insurance markets. Traditional index insurance products have suffered from low adoption rates and implementation difficulties, primarily attributed to the complex, nonlinear relationships between weather variables and crop yields that conventional linear models fail to capture. This research leverages the universal approximation capabilities of neural networks to model high-dimensional weather-yield relationships through a comprehensive risk measurement minimization framework. The methodology employs a multi-layer neural network architecture with penalty-based constrained optimization, enabling the capture of intricate weather patterns while ensuring contract feasibility and regulatory compliance. The framework formulates the problem as a risk measurement minimization challenge that explicitly incorporates both farmer and insurer perspectives through a unified objective function, ensuring that resulting contracts remain commercially viable for insurance providers while effectively managing farmers' exposure to weather risks. A Utility Optimization Model (UOM) is also implemented as a comparative benchmark, following established approaches in weather index insurance literature. Empirical validation using Iowa soybean production data demonstrates the framework's effectiveness in capturing complex weather-yield relationships, with comprehensive sensitivity analyses confirming robustness across different risk measures and market conditions. The neural network approach successfully models the intricate, nonlinear relationships between various weather variables and crop yields, enabling more accurate risk assessment and more effective risk transfer compared to traditional linear approaches.

The second study introduces a budget-constrained semi-dynamic framework for optimal reinsurance design that bridges the gap between static single-period models and fully dynamic approaches. This research proves the optimality of stop-loss reinsurance contracts under various dependency structures between claims, extending classical results to accommodate random claim numbers and arrival times while maintaining analytical tractability. The theoretical framework addresses both independent and dependent claim scenarios, with the latter employing robust optimization techniques that identify comonotonicity as the worst-case dependence structure. For risk-neutral insurers, the analysis establishes optimal deductible allocation rules based on stochastic orderings of claim severity and arrival times, demonstrating that larger deductibles should be allocated to claims with higher severity but shorter arrival times. The framework incorporates realistic constraints including budget limitations and temporal discounting effects, providing practical guidance for insurers managing multiple risks under semi-dynamic conditions. Extensive numerical experiments validate the theoretical predictions and demonstrate the framework's effectiveness across different parameter settings, with sensitivity analyses revealing the impact of discount rates, safety loadings, and budget constraints on optimal allocation strategies.

The connection between these research directions lies in their shared focus on developing sophisticated risk transfer mechanisms that balance multiple stakeholder interests while incorporating practical implementation constraints. Both studies demonstrate how advanced analytical techniques can be effectively applied to traditional insurance problems, providing new tools for contract design and risk optimization. The neural network framework advances beyond conventional linear modeling approaches by capturing complex nonlinear relationships through machine learning techniques, while the semi-dynamic reinsurance model extends existing theory to more realistic multi-claim scenarios with temporal considerations and budget constraints.

Through theoretical development, methodological innovation, and empirical validation, this thesis contributes to both academic literature and practical applications of insurance risk management. The frameworks developed provide scalable solutions that can be adapted to various insurance contexts, with potential applications extending beyond agricultural insurance to other weather-sensitive sectors and beyond single-period reinsurance to dynamic risk management strategies. The research demonstrates how sophisticated mathematical frameworks can address fundamental challenges in modern insurance markets while maintaining practical implementability, offering pathways for future developments in this critical field.

Keywords: Neural networks, weather index insurance, optimal reinsurance, risk management, agricultural insurance, stochastic optimization, convex ordering