AI-Native Insurance Framework for Agentic AI Deployments

The rise of autonomous AI systems, or agentic AI, introduces novel insurance challenges due to their decision-making capabilities, tool invocation, and interaction with external environments. This research proposes a mathematical framework specifically designed for AI-native insurance, covering underwriting, pricing, and contract design for these deployments. The framework represents an AI deployment through a "risk state," which encompasses factors like autonomy level, operational authority, permission exposure, governance maturity, and dependency concentration. This risk state is then mapped to various financial parameters, including event probabilities, potential loss severities, governance costs, premiums, deductibles, and coverage allocations. The paper formulates an optimization problem for designing insurance contracts that satisfy participation, profitability, and incentive compatibility constraints. It also explores the structural properties of insurability, such as defining an insurability region and demonstrating how feasibility deteriorates with increased exposure, while governance certification can mitigate risks. The study includes a healthcare case study to illustrate contract optimization and automated claims processing for agentic AI.