# Foundations of a Time-Consistent Counterfactual Actuarial Runtime for Autonomous AI Agents

arXiv: https://arxiv.org/abs/2605.26508 · HTML: https://mlsanity.com/paper/2605.26508/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 8 of 8)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Optimizing the CVaR via Sampling](https://mlsanity.com/paper/1404.3862/) (2014)
- [Algorithms for CVaR Optimization in MDPs](https://mlsanity.com/paper/1406.3339/) (2014)
- [Quantifying Trust: Financial Risk Management for Trustworthy AI Agents](https://mlsanity.com/paper/2604.03976/) (2026)
- [Algorithmic Insurance](https://mlsanity.com/paper/2106.00839/) (2021)
- [Insuring Every Action: An Authority Frontier Framework for Runtime Actuarial Control of Autonomous AI Agents](https://mlsanity.com/paper/2605.25632/) (2026)
- [Catastrophe Insurance: An Adaptive Robust Optimization Approach](https://mlsanity.com/paper/2405.07068/) (2024)

## Built on by (most cited first, 3 of 3)

- [When Agent Automation Becomes Profitable: Quantifying and Insuring Autonomous AI Risk through Trace-Economic Underwriting](https://mlsanity.com/paper/2606.16465/) (2026)
- [Gaming-Resistant Insurance Contracts for Autonomous AI Agents: Strategy-Proof Toll Mechanism Design](https://mlsanity.com/paper/2606.16326/) (2026)
- [agent-risk: Risk Assessment for Changes to AI Agents](https://mlsanity.com/paper/2610.16280/) (2026)

## Abstract (arXiv)

We propose a foundational runtime actuarial layer for autonomous AI agents in which every side-effect-bearing action carries a time-consistent, counterfactual risk toll computed against a contractually fixed safe default, inside an explicit underwriting boundary. The framework treats per-action insurance as the primary unit of analysis and replaces post-hoc annual liability cover with a pre-action transaction layer. The paper establishes four structural results: (i) a well-defined counterfactual toll under a chosen safe-default mapping and continuation policy, with explicit non-uniqueness; (ii) a no-splitting property within an underwriting boundary that telescopes path-decomposed actions into a boundary potential, with a corollary tying gaming-resistance to boundary design; (iii) an irreversible-authority premium, split into a strictly positive action-level component and an if-and-only-if characterisation of the set-level robust capital increase; and (iv) a conservative runtime gating theorem that translates high-probability toll envelopes into an executed-action budget guarantee. The result is the mathematical base layer for a broader program: an empirical companion instantiates the runtime through an Actuarial Action Interface and authority-frontier experiments; a mechanism-design companion studies strategic operator incentives and cross-boundary aggregation; and a dynamic-underwriting companion studies experience rating and audit-replay calibration. The present paper states the primitive contract, the toll identity, the within-boundary no-arbitrage result, and the budget guarantee on which those later layers depend.