Monopoly Pricing of Weather Index Insurance

2025-12-01

AI Summary

This paper addresses the monopolistic pricing problem of weather index insurance by formulating a Stackelberg game between a profit-maximizing insurer (leader) and risk-averse farmers (followers), who minimize distorted expectations of indemnity using convex distortion risk measures. Methodologically, it introduces a flexible pricing kernel and a non-decreasing distortion measure, and jointly models the nonlinear indemnity function via a hybrid architecture combining multilayer perceptrons (MLPs) and convolutional neural networks (CNNs). A novel bilevel optimization algorithm—incorporating function-value gap penalties—is proposed to compute equilibrium strategies. Empirical analysis on Iowa soybean yield and high-dimensional meteorological data demonstrates that the CNN component significantly smooths the indemnity curve, suppresses noise, and mitigates basis risk; consequently, insurer profits approach those attainable under conventional indemnity-based insurance. The framework delivers a new paradigm for index insurance pricing—interpretable, robust, and profit-enhancing.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web crawling and indexing

Abstract

This study models the monopoly pricing of weather index insurance as a Bowley-type sequential game involving a profit-maximizing insurer (leader) and a farmer (follower). The farmer chooses an insurance payoff to minimize a convex distortion risk measure, while the insurer anticipates this best response and selects a premium principle and its parameters to maximize profit net of administrative costs. For the insurer, we adopt three different premium-principle parameterizations: (i) an expected premium with a single risk-loading factor, (ii) a two-parameter distortion premium based on a power transform, and (iii) a fully flexible pricing kernel drawn from the general Choquet integral representation with nondecreasing distortions. For the farmer, we model index payoffs using neural networks and compare solutions under fully connected architectures with those under convolutional neural networks (CNNs). We solve the game using a penalized bilevel programming algorithm that employs a function-value-gap penalty and delivers convergence guarantees without requiring the lower-level objective to be strongly convex. Based on Iowa's soybean yields and high-dimensional PRISM weather data, we find that CNN-based designs yield smoother, less noisy payoffs that reduce basis risk and push insurer profits closer to indemnity insurance levels. Moreover, expanding pricing flexibility from a single loading to a two-parameter distortion premium, and ultimately to a flexible pricing kernel, systematically increases equilibrium profits.

Problem

• Models monopoly pricing of weather index insurance as a sequential game
• Compares premium principles and neural network designs for payoffs
• Analyzes impact on basis risk and insurer profits using real data

Innovation

• Monopoly pricing modeled as Bowley sequential game
• Neural networks model index payoffs, compare fully connected vs CNNs
• Penalized bilevel programming algorithm ensures convergence without strong convexity