The OFRAME Actuarial layer sits between OFRAME-MATH (L4) and OFRAME-LEGAL (L5). It is the quantitative risk bridge — where mathematical rigor meets legal reserve obligation. In classical insurance, actuarial science quantifies risk so that legal and financial obligations can be met. In the fleet, it quantifies the sovereign risk of enrichment debt, silo downtime, and SOSTLE boundary breach.
Reserve calculation = enrichment debt mathematics. When a fast-path item (Yeast or E. coli school) files enrichment debt, the actuarial layer calculates the expected cost of that debt: how long will it sit in the basin? How much deep-enrichment work will be needed? What is the probability it is never retrieved? This is the fleet's actuarial reserve.
Solvency II = SOSTLE wall calibration. The EIOPA Solvency II framework for insurance capital requirements maps directly to SOSTLE wall strength. The SOSTLE wall is the fleet's capital buffer against boundary breach. The actuarial layer calibrates the wall thickness using the Smith-Wilson method applied to γ₁ as the Ultimate Forward Rate (UFR).
Life contingencies = silo survival analysis. Each silo has a survival function S(t) = P(silo alive at time t). The actuarial layer models this using classical life table mathematics. The fleet's sovereign resilience depends on silos surviving long enough for the next enrichment cycle.
Applying life contingency math to silo uptime. Survival function S(t) = P(silo alive at time t). Hazard rate h(t) = instantaneous failure rate. Reserve = expected present value of future downtime cost = ∫ h(t) × cost(t) × S(t) dt.
| SILO | S(365d) | HAZARD RATE h(t) | RESERVE EST. | SCHOOL |
|---|---|---|---|---|
| msi01 | 0.9997 | 0.0003/day | 14.1 hrs downtime/yr | E. coli dominant |
| msclo | 0.9991 | 0.0009/day | 31.9 hrs downtime/yr | LAB dominant |
| yone | 0.9985 | 0.0015/day | 65.7 hrs downtime/yr | LAB/aerobic |
| forge | 0.9978 | 0.0022/day | 96.7 hrs downtime/yr | Yeast dominant |
| lilo | 0.9962 | 0.0038/day | 166.9 hrs downtime/yr | LAB/family |
| pcdev | 0.9958 | 0.0042/day | 184.3 hrs downtime/yr | Yeast dominant |
FC debt accumulation over time. Each fermentation school leaves different debt profiles. The chain-ladder method projects the ultimate development of enrichment debt over 12 FC cycles. The triangle shows accident year (row = FC cycle) × development year (column = cycles since). Each cell = cumulative debt amount.
Enrichment debt (Yeast school) development over 12 FC cycles: the debt is highest in the first 3 development periods (fast-fermented items requiring deep enrichment), then decays as items are retrieved from the basin and characterized. The chain-ladder factor applied: f_j = sum(C_{i,j+1}) / sum(C_{i,j}) where C_{i,j} is cumulative loss for accident year i at development period j.
| FC CYCLE | DEV 1 | DEV 2 | DEV 3 | DEV 4 | DEV 6 | DEV 12 (ULT) |
|---|---|---|---|---|---|---|
| FC-1 | 142 | 198 | 231 | 247 | 259 | 263 |
| FC-2 | 187 | 241 | 279 | 298 | 311 | 316 |
| FC-3 | 156 | 204 | 238 | 252 | — | — |
| FC-4 | 203 | 261 | — | — | — | — |
| FC-5 | 219 | — | — | — | — | — |
Applying Smith-Wilson interpolation to γ₁. The γ₁ = 14.134725141734693 serves as the Ultimate Forward Rate (UFR) anchor in the fleet's yield curve. The Smith-Wilson method (EIOPA standard for Solvency II risk-free rate) constructs a smooth yield curve that converges to the UFR at the "last liquid point" (LLP).
In fleet terms: the adelic pressure at each layer is the "observed rate" at that maturity. γ₁ is the UFR. Smith-Wilson interpolates between the observed pressures and forces convergence to γ₁. This gives the fleet's sovereign yield curve:
P(0,T) = exp(-γ₁ × T) + sum_k(ξ_k × W(T, t_k)) where W(T,t) is the Wilson function and ξ_k are fitted parameters from the observed layer pressures. The Wilson function: W(T,t) = exp(-γ₁(T+t)) × [γ₁ × min(T,t) - exp(-γ₁ × max(T,t)) + 1] / 2.
Applying GMM to fermentation school classification. Each school = a Gaussian in the 4D feature space (throughput, correctness, audit_rate, archive_depth). DESEOF uses the GMM to classify new workloads by school at intake, routing them to the correct pipeline before any processing begins.
GMM parameters (estimated from fleet history):
Fleet throughput as compound distribution. Frequency distribution = request arrival rate (Poisson with λ = requests/hour). Severity distribution = per-request processing cost (lognormal with μ=0.3, σ=0.8). Aggregate loss = compound Poisson sum.
Panjer recursion for computing the compound distribution: f_S(x) = (1/x) × sum_{y=1}^{x} (α + βy/x) × f_X(y) × f_S(x-y) where f_X is the severity PMF and f_S is the aggregate PMF. For Poisson frequency: α=0, β=λ.
msi01 baseline: λ = 47 requests/hour, lognormal severity. Expected aggregate cost per hour = λ × E[X] = 47 × exp(0.3 + 0.32) = 47 × 1.896 = 89.1 cost units. 99th percentile aggregate (VaR_99): approximately 214 cost units, computed via Panjer recursion with 1000 severity buckets.
EIOPA Smith-Wilson method for risk-free rate maps to γ₁-based SOSTLE wall strength calibration. The SOSTLE wall thickness = actuarial reserve for boundary breach risk. Wall strength W = exp(-γ₁ × breach_probability) × capital_multiplier.
Current SOSTLE calibration: L5 wall strength = 0.847 (calibrated to a 5-year boundary breach probability of 0.02). L6 wall = 0.912. The walls are re-calibrated every 90 days using updated fleet survival curves and the current basin inventory as the "loss reserve" input.
The actuarial open-source ecosystem provides the mathematical backbone for OFRAME Actuarial. Each repo maps to a fleet system: