Adaptive Precision and Stopping

The engine's non-adaptive intervals are fixed-sample: Wilson intervals for probabilities, bootstrap intervals for quantiles and shortfall. They are correct exactly once, at a path count declared before the run starts.

Checking such an interval repeatedly and stopping the first time it looks narrow enough inflates the false-convergence rate without bound, because the stopping time is chosen by looking at the same noise the interval is meant to describe. The fix is a confidence sequence: an interval construction that holds simultaneously at every sample size, so any stopping rule, including one that peeks at every checkpoint, inherits the stated coverage.

Clients pick a named tier, never a confidence level or a tolerance. The scientific target behind a name is identical across plans, so a cheaper tier reaches its ceiling and reports nonconvergence rather than quietly making the same claim from a looser interval. Checkpoints occur every 10,000 paths.

The authorized ceiling is , floored to a whole logical block. A client value can only reduce the ceiling: naming a tier selects a policy, it does not entitle the caller to that tier's compute.

{
  "path_count": 10000,
  "precision": { "tier": "enterprise_tail", "max_paths": 80000 }
}

With precision set, path_count is no longer the number of paths simulated. The artifact reports both the budget and the actual count, along with the stop reason.

The joint error budget across the primary family is , split by Bonferroni over stable metric identifiers. Each member is itself time-uniform, so the split covers every checkpoint of every primary metric simultaneously. There is no additional penalty for how often the coordinator looks.

The paired tier estimates the quantile of the pathwise difference, not the difference of two marginal quantiles. Because both arms advance over identical shock coordinates, path in one is path in the other, and the difference is a genuine per-path contrast:

The two estimands are not equal even at the median, which is why the metric identifiers say pathwise. Reporting one under the other's name would be a different quantity, not a rounding difference.

The paired tier binds on four families rather than one. A tier whose only binding metric is a probability stops as soon as that probability is precise, which can leave the wealth difference the comparison was really about far too wide to act on.

The v3 policy carried provisional widths chosen by judgment. The v3 sweep exhausted every tier ceiling without converging, and the measured worst widths falsified seven of them. mc-precision-v4replaces those with values measured through the production engine on an orthogonal grid: four tiers, four representative generator families, 5/15/20/40-year horizons, and 5 and 10-asset diversified and concentrated portfolios, with static solver weights, annual HRP and HERC refits, monthly trading, SIP and SWP, FIFO tax, fees and deterministic stress arms.

Under v4 all eight grid cells met every joint primary target, at 50,000, 50,000, 40,000, 60,000, 100,000, 90,000, 80,000 and 50,000 paths respectively. Comparative local wall time fell from 2,717.4 to 1,944.7 seconds, a 28.4% reduction, while the two hardest tail cells still needed 100,000 and 90,000 paths.

The study also caught two defects worth naming. Pathwise quantile differences use the ordinary finite-sample order-statistic mixture, but their specifications named a method that did not exist, so the stopping gate correctly refused them at every width. Separately, a model-risk comparison interval divides error across metrics and generators, so it can remain inadmissible after the selected generator has met its own tier. Comparison arms now continue independently to the next checkpoint until those stricter simultaneous intervals meet their per-metric targets or hit the ceiling.

Changing any target bumps the policy version, because the policy digest is published in every adaptive run's convergence block and consumers key their claims off it.