arXiv:2607.13230v1 Announce Type: new Abstract: Agentic AI introduces new insurance challenges because 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. 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, and formulates an optimization problem for insurance contract design under participation, profitability, and incentive compatibility constraints. 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. A healthcare case study illustrates contract optimization, sensitivity analysis, and automated claims processing for agentic AI systems.
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