Decision-Centric Large Deviations for Data-Driven Capital Buffers in Ruin Models

What the math gives to ML

The paper develops a decision rule for rare-event constraints when the parameter governing future risk is estimated from finite historical data. Its key transferable asset is the explicit large-deviation coupling between an atypical estimate and the future failure event: a threshold must pay both the KL cost of observing the estimate and the exponential cost of the future excursion. This suggests replacing plug-in safety thresholds in sequential ML systems with an envelope computed from an empirical rate and a target failure exponent. The most practical first application is online monitoring or reinforcement-learning safety, where a model must choose a buffer for future cumulative violations rather than treating an estimated violation probability as known.