Stochastic frontier variant axis

The spending level or retirement age each frontier variant was built with (grid multipliers 0.85..1.15 of spending; -2..+2 years of retirement age).

Field: Frontier variant value Unit: US dollars Basis: nominal dollars Computed by: Engine Status: Complete chain

Appears in: monte-carlo-page (Frontier charts x-axis (spending dollars; retirement age))

Calculation records

• Stochastic frontier axis value per variant Data record, justified by derivation

  Purpose: What the x of a frontier point means: the caller's own grid value, not anything read back out of the stochastic result.

  Statement: Each frontier point's x is the caller's grid value for that variant. For buildSpendingSuccessFrontier it is the variant plan's expenses.baseAnnual, that is max(0, round(baseAnnual x multiplier)); for buildRetirementAgeSuccessFrontier it is the lowest resulting retirement age among the people who have one, each moved by the caller's delta and clamped to [30, 80], or 0 when nobody has a retirement age. Neither is inferred from the point's stochastic row. For baseAnnual $60,000 with multipliers 0.8, 1.0 and 1.2 the axis is $48,000, $60,000 and $72,000; for deltas -2, 0 and 3 on a one-person plan retiring at 65 the axis is 63, 65 and 68; for two people at 65 and 62 with delta +3 it is 65; for age 31 with delta -2 it is 30. Units: usd on the spending axis, years on the retirement-age axis. Rounding: the spending variant rounds to whole dollars and floors at 0; the retirement-age variant clamps to [30, 80] and is not otherwise rounded.

  Formula: x_spending(i) = max(0, round(baseAnnual x multiplier_i)); x_retirementAge(i) = min over people p with a retirement age of clamp(age_p + delta_i, 30, 80), or 0 when no person has one

  • baseAnnual: Base plan's annual base expenses (unit: usd) (domain: worksheet 60,000)
  • multiplier_i: Caller's spending multiplier for variant i (unit: 1) (domain: worksheet 0.8, 1.0, 1.2)
  • delta_i: Caller's signed retirement-age change for variant i, applied to each person's planned retirement age (unit: years) (domain: worksheet -2, 0, 3)
  • age_p: Person p's planned retirement age (unit: years) (domain: worksheet 65; 65 and 62; 31)

  Timing: once per variant, when the frontier builds its plan set

  Rounding: spending rounds to whole dollars and floors at 0; the retirement-age result is clamped to [30, 80] and not otherwise rounded

  Limits:

  • The two axes are not the same quantity: the spending axis is the variant's absolute base annual expense, while the retirement-age axis is the resulting planned age, so neither axis is a delta from the base: not -12,000, 0 and 12,000, and not -2, 0 and 3
  • A frontier sweep is capped at MAX_FRONTIER_POINTS (15) points and neither builder searches; the grid is always the caller's
  • A point's other figures (the three success rates, the ending-estate percentiles, expected shortfall) come from the variant's Monte Carlo summary and are not this record's claim; the evidence asserts x only
  • The evidence runs the real builders on a small one-person plan at pathCount 2 and seed 123, the smallest reproducible run the options allow, because the axis does not depend on the stochastic result at all
  • The retirement-age axis was first derived as the caller's delta from the StochasticFrontierPoint.x doc comment, which stated the delta; on 2026-09-18 the comment was corrected to the resulting clamped age the builder publishes, the worksheet was re-derived and re-approved on it, and the evidence pins 63, 65 and 68 for deltas -2, 0 and 3 on a plan retiring at 65, 65 for the two-person case and 30 at the lower clamp

  Provenance: derived by codex, implemented by claude.

  Independent review: cursor

  Gates (6 of 6 pass): fixture registers a test: pass; pins resolve: pass; families exist: pass; worksheet exists: pass; mutation receipt exists: pass; provenance independent: pass

  Worksheet: monte-carlo-stochastic-frontier-axis.md Mutation receipt: monte-carlo-stochastic-frontier-axis.mutation.md

  Evidence tests: frontiers.evidence.test.ts

  Implemented in: frontiers.ts

  Is the number of: stochastic-frontier-variant-axis

Engine source: engine/src/montecarlo/frontiers.ts (StochasticFrontierPoint.x)