Abstract
Agentic AI introduces new insurance challenges as autonomous AI systems can make decisions, invoke tools, modify external environments, and interact with third-party services. This paper develops an AI-native mathematical framework for underwriting, pricing, and contract design for agentic AI deployments.
Risk State Modeling
A deployment is represented by a risk state that captures autonomy level, operational authority, permission exposure, governance maturity, and dependency concentration. The framework maps the risk state to event probabilities, loss severities, governance costs, premiums, deductibles, coverage allocation, and policy covenants, formulating an optimization problem for insurance contract design under participation, profitability, and incentive compatibility constraints.
Structural Properties of Insurability
The paper establishes structural properties of insurability, including characterization of an insurability region, monotone deterioration of feasibility with increasing exposure, and governance certification thresholds. Insurance is further interpreted as both an operational cost and a regulatory mechanism for AI deployment.
Case Study
A healthcare case study illustrates contract optimization, sensitivity analysis, and automated claims processing for agentic AI systems.
Blogger's Review: This paper provides a comprehensive theoretical foundation for insurance in the context of agentic AI, particularly in risk management and contract design, which is of significant practical value. The inclusion of real-world case analysis enhances the operability of the theory, laying a foundation for the future AI insurance market.