Algorithmic Insurance

Abstract

When AI systems make errors in high-stakes domains like medical diagnosis or autonomous vehicles, a single algorithmic flaw across varying operational contexts can generate highly heterogeneous losses that challenge traditional insurance assumptions. Algorithmic insurance constitutes a novel form of financial coverage for AI-induced damages, representing an emerging market that addresses algorithm-driven liability. However, insurers currently struggle to price these risks, while AI developers lack rigorous frameworks connecting system design with financial liability exposure. We analyze the connection between operational choices of binary classification performance to tail risk exposure. Using conditional value-at-risk (CVaR) to capture extreme losses, we prove that established approaches like maximizing accuracy can significantly increase worst-case losses compared to tail risk optimization, with penalties growing quadratically as thresholds deviate from optimal. We then propose a liability insurance contract structure that mandates risk-aware classification thresholds and characterize the conditions under which it creates value for AI providers. Our analysis extends to degrading model performance and human oversight scenarios. We validate our findings through a mammography case study, demonstrating that CVaR-optimal thresholds reduce tail risk up to 13-fold compared to accuracy maximization. This risk reduction enables insurance contracts to create 14-16% gains for well-calibrated firms, while poorly calibrated firms benefit up to 65% through risk transfer, mandatory recalibration, and regulatory capital relief. Unlike traditional insurance that merely transfers risk, algorithmic insurance can function as both a financial instrument and an operational governance mechanism, simultaneously enabling efficient risk transfer while improving AI safety.

Figures (8)

• Figure 1: The Algorithmic Insurance Business Model.
• Figure 2: Conditional probability $P(Y{=}1 \mid \overline{\gamma})$ under varying model quality (a) and class imbalance (b) in the trigonometric model.
• Figure 3: Divergence between accuracy-maximizing and risk-aware thresholds under asymmetric cost structures. Panels show efficiency gaps (horizontal arrows) and resulting CVaR penalties (text boxes) for false-negative-dominated (left) and false-positive-dominated (right) scenarios.
• Figure 4: Impact of interpretability on residual tail risk. (a) CVaR reduction as a function of interpretability $\zeta$ under different $g(\zeta)$ forms, holding performance gap $\xi = 0.5$. (b) Heatmap of CVaR reduction as a function of $\zeta$ and performance gap $\xi$, assuming a linear $g(\zeta)=\zeta$.
• Figure 5: Decomposition of insurance value components normalized by firm CVaR, showing base value (risk transfer and capital relief) and calibration gains across firm types.

Theorems & Definitions (57)

• Theorem 1: Threshold Characterization
• Proposition 1: Threshold Sensitivity to Cost Asymmetry
• Proposition 2: Threshold Sensitivity to Risk Aversion
• Remark 1: Cost Structure and Threshold Behavior
• Lemma 1: Accuracy-Optimal Threshold
• Definition 1: Threshold Gap Metrics
• Proposition 3: Efficiency–gap Characterization
• Proposition 4: Risk-penalty bounds
• Theorem 2: Insurance Value Decomposition
• Proposition 5: Limit Behavior of Value