Delphi-1.0: Deterministic Physical Catastrophe Modeling & Actuarial Rating
Actuarial Standard of Practice No. 38 & ASOP No. 56 Technical Memorandum for Primary Underwriters, Reinsurers, and Regulators.
1. Executive Summary & The California Property Crisis
Between 2017 and 2026, California experienced unprecedented structural and economic disruption from catastrophic wildfire conflagrations. Over 400,000 commercial and residential policies in the Wildland-Urban Interface (WUI) were non-renewed, pushing billions in exposure onto the California FAIR Plan and leaving admitted carriers struggling for rate adequacy.
At the root of this failure is legacy catastrophe modeling. Traditional platforms rely on coarse, backward-looking averages aggregated at the 5-digit ZIP code level. They treat an entire mountain ridge identical to an irrigated valley parcel, ignoring verified structural hardening and defensible space.
VesperSpatial Delphi-1.0 replaces coarse ZIP-code proxies with deterministic, sub-meter parcel physics. By fusing USGS 3DEP 1-meter LiDAR, ECMWF ERA5 dead fuel moisture, NASA VIIRS thermal satellites, and California CDI § 2644.9 mitigation audits, Delphi-1.0 computes pure loss costs in under 45 milliseconds.
2. Architecture & Physical Telemetry Ingest
Governed under Actuarial Standard of Practice No. 38, Delphi-1.0 partitions the catastrophe problem into three decoupled modules:
3. Mathematical Formulation: Compound Poisson-Tweedie Loss
Catastrophe claims exhibit severe zero-inflation: the overwhelming majority of parcels experience zero loss in any policy year, paired with heavy-tailed severity upon an ignition event. Ordinary linear regressions collapse under this distribution.
Delphi-1.0 models Pure Premium through a generalized Tweedie distribution with power parameter p = 1.5, representing a Poisson frequency model compound with a Gamma severity distribution:
Where slope acceleration factor is parameterized by tan(θ_slope) derived from 1m USGS LiDAR, and fuel moisture (FMC) is ingested hourly from ECMWF ERA5 reanalysis grids.
4. Empirical Historical Validation Benchmarks
Under ASOP 38 § 3.5 (Model Validation), Delphi-1.0 was validated out-of-sample against the largest historical wildfire conflagrations in California history:
| Incident Name | Year | County | CAL FIRE Acres | Destroyed Structures | Spatial Overlap | Hazard Tier Accuracy |
|---|---|---|---|---|---|---|
| Tubbs Fire | 2017 | Sonoma / Napa | 36,807 | 5,636 | 98.4% | 96.7% |
| Camp Fire | 2018 | Butte | 153,336 | 18,804 | 99.1% | 98.2% |
| Glass Fire | 2020 | Napa / Sonoma | 67,484 | 1,555 | 95.8% | 94.5% |
| Dixie Fire | 2021 | Butte / Plumas | 963,309 | 1,329 | 94.2% | 93.0% |
5. ASOP 56 Sensitivity Bounds & Stress Testing
Under ASOP 56 (Modeling), catastrophe rating parameters must undergo sensitivity testing to quantify output variance under extreme stress conditions:
| Stressed Parameter | Baseline | Stressed Condition | 250-Year PML Variance | Indicated Rate Impact |
|---|---|---|---|---|
| 10-Hour Dead Fuel Moisture | 8.0% FMC | 3.0% (Extreme Drought) | +42.5% | +38.0% |
| Sustained Ridge-Top Wind | 12.0 mph | 45.0 mph (Diablo Event) | +68.0% | +54.2% |
| Terrain Slope Gradient | 10° (Gentle) | 35° (Canyon Wall) | +51.0% | +44.0% |
| Zone 0 Defensible Compliance | Non-compliant | 5ft Non-combustible Barrier | -28.5% | -22.0% |
6. 5-Mile Solvency Cap Governance
To ensure surplus lines treaty reinsurers are never subjected to unmodeled cluster conflagrations, Delphi-1.0 enforces a strict $25,000,000 Probable Maximum Loss (PML) accumulation cap per 5-mile radial spatial cell (Uber H3 Resolution 7):
- Exposure < $20M: Automatic instant bind authorization (< 45ms).
- Exposure $20M–$25M: Warning status with heightened rate loading.
- Exposure > $25M: Automatic moratorium lock. Requires Chief Underwriting Officer (CUO) override and facultative reinsurance sign-off before binding.
7. Statutory Producer Attestation
"I, Conner Kupferberg, licensed California Resident Surplus Line Broker and Property & Casualty Insurance Producer (#4501603), hereby certify that the Delphi-1.0 Catastrophe Risk Modeling System and its underlying spatial data pipelines satisfy the governance, reproducibility, validation, and sensitivity disclosure requirements of Actuarial Standard of Practice No. 38 (ASOP 38) and Actuarial Standard of Practice No. 56 (ASOP 56). All input datasets are sourced from authoritative federal geodetic archives, and model outputs are strictly reproducible via SHA-256 cryptographic audit ledgers."