augur: classify trajectories — ruin / forced tier drop / intact

[agentydragon]

The allocation study needs trajectories classified, not scored. Ruin and a forced lifestyle drop are different outcomes, and averaging them into one terminal metric hides the distinction that motivates the whole exercise.

Classes

1. Ruin — could not fund even the survival tier. Already available: augur fails the rollout on an unpayable obligation and records failed_month_index.
2. Forced drop — survived, but only by cutting when you did not choose to. Needs augur: stateful actor — tier state and state-dependent spending #3738; the forced part is the distinction, since the same tier means different things depending on whether the trigger or the arithmetic caused it.
3. Intact — funded the top tier throughout.

Two refinements that carry real information: when the drop happened (45 vs 80 are different lives) and whether it recovered — a drop you climb out of is a bad decade, a permanent one is a different retirement.

What this is for

The headline output is, for each bond-sleeve size, the three probabilities — and specifically how small the sleeve gets before P(ruin) rises off the floor. The cake prices a tiered infinite-horizon floor at ~$4.5M and full-burn-forever at ~$8.8M, both as annuities that fund the worst case deterministically. If the simulated number is materially lower, the annuity framing has been overcharging for certainty, and the difference is real money that could be held in equities.

Two reasons to expect it is:

• Convexity — the last 1% of certainty costs roughly what the first 90% did, because the ladder funds the tail deterministically while equities fund the middle in expectation.
• The 100% was never real — a TIPS ladder is certainty of a cashflow, conditional on never wanting more than the floor, and still carries phantom-income tax risk (now modelled, augur: TIPS — inflation-indexed principal, and the phantom income that decides the muni comparison #3736) and policy risk. Treating one side's residual risk as zero rigs the comparison.

Caveat to keep attached to any number this produces

The result depends on the equity generator's tails. A lognormal GBM understates sequence risk, which makes elasticity look cheaper than it is. "99% is cheap" stays provisional until the equity side has fat tails or a regime component — that is the one place worth spending modelling effort before acting on the output.

Depends on

• augur: stateful actor — tier state and state-dependent spending #3738 (tier state and state-dependent spending) — without it, class 2 is unobservable.
• augur: actor policy — one channel for buys and sells, target allocation over a cash band #3739 (target-allocation liquidation) — without it, the sleeve-size axis does not mean what it says.