What is Probable Maximum Loss (PML)? EP Curves, AAL

Probable maximum loss (PML) is the largest loss an insurer, lender, or investor can reasonably expect from a property or a portfolio. For one building in property underwriting, PML is an engineering estimate of the worst likely fire or explosion. For commercial real estate in earthquake country, PML is a seismic loss estimate built to ASTM International standards. For a portfolio exposed to hurricanes or earthquakes, PML is the loss at a chosen return period, such as the 1-in-100 or 1-in-250 year loss. That loss is read from an exceedance probability (EP) curve, a chart of each loss against its chance of being exceeded in a year. Underwriters, reinsurers, lenders, rating agencies, and regulators use PML to decide how much risk to accept and how much capital to hold. A portfolio PML is one point on that curve. This article makes the case for quoting it with its curve, its basis, and the average loss beyond it.

Key takeaways

• A return period is the inverse of an annual exceedance probability. The 1-in-100 year loss has a 1% chance of being exceeded in any year.
• EP curves come in occurrence exceedance probability (OEP) and aggregate exceedance probability (AEP) forms. OEP tracks the largest event in a year. AEP tracks the total of all events in a year.
• Average annual loss (AAL) is the area under the EP curve. AAL sets the expected-loss part of the premium, and PML sets capital and reinsurance.
• Tail value at risk (TVaR) is the average of every loss beyond the PML. TVaR passes the standard tests for a coherent risk measure, and a single return-period PML can fail them.

What is probable maximum loss?

The term has no single fixed meaning. In a 1969 paper in the Proceedings of the Casualty Actuarial Society, John S. McGuinness called PML "one of the least clear concepts in all insurance." His four-year study collected PML definitions from over one hundred underwriters, and no two fully agreed. Margaret Wilkinson's 1982 paper on estimating PML with order statistics, in the same Proceedings, moved the term toward statistics. She derived six PML estimators. Each starts from the largest sample loss or from a quantile, the loss that a set share of outcomes stays below. Catastrophe models read PML as a quantile today.

PML in property underwriting

The International Risk Management Institute (IRMI) defines PML as a property loss control term for the maximum loss expected at a location in the event of a fire. Marsh describes a PML study as an estimate of the largest physical loss reasonably expected from a single event, including time-related costs.

Property engineers place PML on a ladder of loss estimates for one site:

Estimate	Assumption	Relative size
Normal loss expectancy (NLE)	All protection works as designed	Smallest
Probable maximum loss (PML)	One key protection fails, such as sprinklers	Middle
Maximum foreseeable loss (MFL)	All protection fails	Larger
Maximum possible loss (MPL)	The worst loss that could possibly occur from one event	Largest

Some markets use estimated maximum loss (EML) for a similar rung. Its protection assumptions differ between insurers. A PML or EML figure is comparable only when the survey states which systems fail.

Seismic PML in commercial real estate

Lenders and investors on US commercial property in seismic zones order a seismic risk assessment before closing. ASTM E2026-24, the Standard Guide for Seismic Risk Assessment of Buildings, frames building damage as a probable loss (PL) or scenario loss (SL) assessment. Its companion, ASTM E2557-24, the Standard Practice for Probable Maximum Loss (PML) Evaluations for Earthquake Due-Diligence Assessments, sets the standard of care and reporting for real estate transactions.

For a specified earthquake, the standards replace the single seismic PML with the scenario expected loss (SEL) and the scenario upper loss (SUL). SEL is the mean loss to the building. SUL is the loss with a 90% chance of not being exceeded. The 475-year event is the ground motion with a 10% chance of exceedance in 50 years. For that event, the IRMI guide to seismic risk terms notes that SUL475 matches the traditional PML. Lenders often set limits on SEL475. Under the Fannie Mae Multifamily Guide, Fannie Mae accepts a property with an SEL of 20% or less and requires further analysis between 20% and 40%. It does not buy loans at 40% or more.

Portfolio PML in catastrophe modeling

In catastrophe modeling, PML is the loss at a stated return period for a peril and a portfolio. A reinsurer quoting a "1-in-250 hurricane PML" means the annual loss with a 0.4% chance of being exceeded.

How PML works with return periods and exceedance probability curves

An exceedance probability curve plots each loss amount against the probability that the loss is exceeded in a year. A catastrophe model builds the curve from a stochastic event set: 10,000 or more simulated years of random events. The model runs each year against a portfolio and ranks the yearly losses. In Catastrophe Modeling: A New Approach to Managing Risk (Springer, 2005), Patricia Grossi and Howard Kunreuther treat the EP curve as the main output of a catastrophe model. Karen Clark's 1986 formal approach to catastrophe risk assessment used simulated hurricanes to estimate the losses behind such a curve.

Return periods

The return period is the inverse of the annual exceedance probability. Emil Gumbel's 1941 paper The Return Period of Flood Flows formalized the idea for river floods, and C. Allin Cornell's 1968 Engineering Seismic Risk Analysis carried it to ground motion.

Annual exceedance probability	Return period	Where it is used
10%	1-in-10 years	Earnings volatility
1%	1-in-100 years	US risk-based capital, AM Best stress test
0.5%	1-in-200 years	Solvency II capital
0.4%	1-in-250 years	Reinsurance and rating agency tests
0.21% (10% in 50 years)	1-in-475 years	Seismic SEL and SUL

A return period states a probability. A 1-in-100 year loss can occur two years running. Over 30 years, a 1% annual chance adds up to about a 26% chance of at least one exceedance.

OEP vs AEP

• Occurrence exceedance probability (OEP) ranks each simulated year by its largest single event. It fits per-occurrence reinsurance, which pays per event.
• Aggregate exceedance probability (AEP) ranks each year by the sum of all its events. It fits annual aggregate covers and capital tests, which both measure the whole year's loss.

At any return period, the AEP loss is greater than or equal to the OEP loss. The gap widens for perils with several damaging events a year. The National Oceanic and Atmospheric Administration (NOAA) billion-dollar disasters list records Harvey, Irma, and Maria in the 2017 Atlantic season. An annual aggregate cover adds those three losses together, and a per-occurrence cover responds to each one separately.

AAL as the area under the EP curve

Average annual loss is the mean loss per year across all simulated years. It is also the area under the AEP curve when the curve is drawn with probability on one axis and loss on the other. Each of N simulated years carries a probability of 1/N. Summing each year's loss × 1/N gives the area, and the same sum gives the mean. AAL sets the technical premium, the part of the price that covers expected losses. PML comes from the tail of the same distribution, the rare high-loss years. It sets the capital and reinsurance an insurer holds to survive a bad year.

TVaR as the average beyond the PML

A return-period PML is a quantile. In risk-measure terms, the 1-in-100 loss is value at risk (VaR) at 99%. Tail value at risk (TVaR) is the average of all losses at or beyond that quantile. It is also called tail conditional expectation (TCE), conditional value at risk, or expected shortfall.

Philippe Artzner, Freddy Delbaen, Jean-Marc Eber, and David Heath set out four axioms for a coherent risk measure in Coherent Measures of Risk (Mathematical Finance, 1999). The axioms are monotonicity, translation invariance, positive homogeneity, and subadditivity. Subadditivity says that combining two portfolios never needs more capital than holding them apart. A quantile can fail it. Two portfolios that each have a small chance of a large loss can each have a 1-in-100 PML of zero while the combined portfolio has a positive one. Carlo Acerbi and Dirk Tasche proved in On the coherence of expected shortfall (Journal of Banking and Finance, 2002) that expected shortfall is coherent for general loss distributions. The same year, R. Tyrrell Rockafellar and Stanislav Uryasev showed in Conditional value-at-risk for general loss distributions that it can be minimized with linear programming.

Regulators have moved toward the average. The Swiss Solvency Test (SST) sets target capital as a one-year expected shortfall at 99%. The rule is in the technical document on the SST from FINMA, the Swiss Financial Market Supervisory Authority. For bank trading books, the Basel Committee's minimum capital requirements for market risk replaced 99% VaR with 97.5% expected shortfall.

Probable maximum loss examples

• Reinsurance purchase. The main purpose of PML in reinsurance is to set the size of the program. An insurer buys catastrophe excess-of-loss cover, which pays the part of an event loss above a set amount, up to its 1-in-100 or 1-in-250 OEP loss. Reinsurers price each layer from the part of the EP curve it covers.
• Lloyd's Realistic Disaster Scenarios (RDS). Lloyd's asks every syndicate to report its loss from a fixed set of scenarios. The RDS 2026 Scenario Specification defines a Gulf of Mexico windstorm with an industry insured loss of US$113 billion onshore and US$7.1 billion offshore. RDS losses come from fixed scenarios with no return period, separate from the model's return-period PMLs.
• Solvency II. Article 101 of Directive 2009/138/EC calibrates the Solvency Capital Requirement to the value at risk of basic own funds at a 99.5% confidence level over one year. That is a 1-in-200 year loss. A European insurer's catastrophe capital starts from its 1-in-200 AEP.
• US risk-based capital. The National Association of Insurance Commissioners (NAIC) catastrophe risk charge (Rcat) uses the worst year in 100 for earthquake and hurricane, per the NAIC Catastrophe Risk Subgroup materials.
• Rating agencies. In Catastrophe Analysis in AM Best Ratings, AM Best runs a stressed BCAR (Best's Capital Adequacy Ratio). The stress cuts reported surplus by the 1-in-100 year net, post-tax, per-occurrence PML across all perils. That is an OEP number. The test shows whether an insurer keeps its rating after one bad event.
• Commercial real estate. A lender reviewing a Los Angeles office building reads the SEL475 and SUL475 from an ASTM E2557 report and applies the Fannie Mae thresholds above.
• Catastrophe bonds. Investors in a catastrophe bond read the attachment and exhaustion points as return periods on the sponsor's EP curve. The two points are the losses where principal starts to go and where it is gone. Those return periods give the chance of losing principal.

Hurricane Ike made landfall near Galveston Island, Texas, in September 2008 as a large Category 2 hurricane, per the National Hurricane Center's Tropical Cyclone Report. Galveston County is the exposure for the walkthrough below.

How PML is calculated

A catastrophe model produces portfolio PML from exposure, hazard, vulnerability, and a ranked table of yearly losses:

1. Exposure. Geocode every insured location and record its construction, occupancy, year built, and replacement value. Building footprints and parcel data fill in what a policy record leaves out.
2. Hazard. Run a stochastic event catalog: thousands of synthetic hurricanes, earthquakes, floods, or wildfires, each with a footprint of wind speed, shaking, depth, or flame length. Flood footprints depend on terrain from a digital elevation model, and analysts check footprints against real events mapped from Earth observation data such as radar imagery.
3. Vulnerability and financial terms. Convert hazard intensity at each location into a damage ratio, then apply deductibles, limits, and reinsurance.
4. Rank the years. Sum losses by simulated year for AEP, or take each year's maximum for OEP, then read the loss at each return period and average the tail for TVaR.

Steps 1 and 2 are spatial. Each location must be matched to the hazard footprints that touch it. A large portfolio against a large catalog means billions of location-event pairs.

Probable maximum loss in Wherobots

WherobotsDB runs steps 1 and 2. It geocodes and enriches exposure, then joins it to hazard rasters and footprints for a whole portfolio. It handles raster and vector data in one engine; most stacks pick one. In one project, Wherobots scored every building in Colorado against five perils and the parcels the buildings sit on. That is 2,771,126 Overture buildings, with results published as the Colorado property risk explorer. A spatial join attaches each building to its hazard values. A raster zonal statistic such as RS_ZonalStats samples flood depth or wildfire grids under each footprint.

The walkthrough below runs the whole PML chain in one SQL statement. It is a toy: the exposure is real, and everything else is made up. The query read two Overture tables and generated the rest in SQL:

Input	Source and format	Size	What the query read
Buildings	Overture buildings_building, an Iceberg table in the Wherobots open data catalog	164,411 buildings whose centroid falls in the county	Footprint geometry and bounding box. Footprint area in square metres stands in for replacement value
County boundary	Overture divisions_division_area, an Iceberg table in the same catalog	1 polygon	The Galveston County land polygon, selected by id
Event set	Generated in SQL with sequence() and seeded rand()	10,000 years, 100,000 candidate events, 10,003 kept	Event center, uniform in the county's bounding box; radius, 500 m plus an exponential draw with a 2 km mean; peak damage ratio, 10% to 60%
Poisson table	Generated in SQL	10 rows, k = 0 to 9	Cumulative probability of each yearly event count

• Event set. A seeded rand(7) draws each year's event count from a Poisson distribution (independent random arrivals) with a mean of one. rand(11) to rand(14) draw each event's center, radius, and peak damage ratio, the share of value lost at the center.
• Vulnerability. The damage ratio falls linearly from the peak at the center to zero at the edge. Loss is building area times damage ratio, summed per event: square metres of damaged footprint.
• Statistics. OEP takes each year's largest event, AEP sums the year, AAL averages all years, PML reads a rank, and TVaR averages every year at or above that rank.

EXPLAIN FORMATTED showed broadcast spatial index joins and no Cartesian product, a step that pairs every row with every row.

-- Toy illustration: 10,000 seeded years of circular windstorm footprints over Galveston County, TX.
-- Exposure is real (Overture buildings). The events, damage curve and loss unit are made up.
WITH pois AS (
  -- Poisson CDF for a mean of 1 event per year, k = 0 to 9
  SELECT k, SUM(EXP(-1.0) / FACTORIAL(k)) OVER (ORDER BY k) AS cdf
  FROM (SELECT explode(sequence(0, 9)) AS k)
),
years AS (
  SELECT sim_year, rand(7) AS u
  FROM (SELECT explode(sequence(0, 9999)) AS sim_year)
),
year_n AS (
  -- Inverse-CDF draw: the event count is the number of k whose CDF lies below u
  SELECT /*+ BROADCAST(p) */ y.sim_year, COUNT(p.k) AS n_events
  FROM years y LEFT JOIN pois p ON p.cdf < y.u
  GROUP BY y.sim_year
),
slots AS (
  -- 10 candidate events per year: a uniform center in the county box, a radius of
  -- 500 m plus an exponential draw with a 2 km mean, and a peak damage ratio of 10% to 60%
  SELECT event_id DIV 10 AS sim_year, event_id, event_id % 10 AS k,
         -95.234 + 0.864 * rand(11) AS lon,
          29.084 + 0.515 * rand(12) AS lat,
         500 - 2000 * LN(1 - rand(13)) AS radius_m,
         0.10 + 0.50 * rand(14) AS peak_dr
  FROM (SELECT explode(sequence(0, 99999)) AS event_id)
),
centers AS (
  SELECT s.sim_year, s.event_id, s.radius_m, s.peak_dr,
         ST_Transform(ST_Point(s.lon, s.lat), 'EPSG:4326',
                      '+proj=utm +zone=15 +datum=WGS84 +units=m +no_defs') AS c
  FROM slots s JOIN year_n y ON s.sim_year = y.sim_year AND s.k < y.n_events
),
footprints AS (
  SELECT *, ST_Buffer(c, radius_m) AS fp FROM centers
),
county AS (
  SELECT geometry AS g FROM wherobots_open_data.overture_maps_foundation.divisions_division_area
  WHERE id = '8936ce65-efd3-4e5a-9917-947f20ff540b'   -- Galveston County, Texas (land polygon)
),
buildings AS (
  -- Exposure: footprint area in m2 stands in for replacement value
  SELECT /*+ BROADCAST(c) */ b.id,
         ST_Transform(ST_Centroid(b.geometry), 'EPSG:4326',
                      '+proj=utm +zone=15 +datum=WGS84 +units=m +no_defs') AS pt,
         ST_Area(ST_Transform(b.geometry, 'EPSG:4326',
                      '+proj=utm +zone=15 +datum=WGS84 +units=m +no_defs')) AS area_m2
  FROM wherobots_open_data.overture_maps_foundation.buildings_building b, county c
  WHERE b.bbox.xmin > -95.235 AND b.bbox.xmax < -94.369
    AND b.bbox.ymin > 29.083 AND b.bbox.ymax < 29.600
    AND ST_Intersects(c.g, ST_Centroid(b.geometry))
),
event_loss AS (
  -- Damage ratio falls linearly from peak_dr at the center to 0 at the edge
  SELECT f.sim_year, f.event_id,
         SUM(b.area_m2 * f.peak_dr * (1 - ST_Distance(f.c, b.pt) / f.radius_m)) AS loss
  FROM footprints f JOIN buildings b ON ST_Contains(f.fp, b.pt)
  GROUP BY f.sim_year, f.event_id
),
annual AS (
  SELECT y.sim_year, y.n_events,
         COALESCE(SUM(e.loss), 0) AS aep_loss,   -- total of all events in the year
         COALESCE(MAX(e.loss), 0) AS oep_loss    -- largest single event in the year
  FROM year_n y LEFT JOIN event_loss e ON y.sim_year = e.sim_year
  GROUP BY y.sim_year, y.n_events
),
exposure AS (
  SELECT COUNT(*) AS buildings, ROUND(SUM(area_m2)) AS exposed_m2 FROM buildings
),
ranked AS (
  SELECT *, ROW_NUMBER() OVER (ORDER BY aep_loss DESC) AS aep_rank,
            ROW_NUMBER() OVER (ORDER BY oep_loss DESC) AS oep_rank
  FROM annual
)
SELECT /*+ BROADCAST(x) */
       FIRST(x.buildings)                                      AS buildings,
       FIRST(x.exposed_m2)                                     AS exposed_m2,
       COUNT(*)                                                AS years,
       SUM(n_events)                                           AS events,
       SUM(CASE WHEN aep_loss = 0 THEN 1 ELSE 0 END)           AS zero_loss_years,
       ROUND(AVG(aep_loss))                                    AS aal,
       ROUND(MAX(CASE WHEN aep_rank = 1000 THEN aep_loss END)) AS aep_10,
       ROUND(MAX(CASE WHEN oep_rank = 100 THEN oep_loss END))  AS oep_100,
       ROUND(MAX(CASE WHEN aep_rank = 100 THEN aep_loss END))  AS aep_100,
       ROUND(MAX(CASE WHEN oep_rank = 50  THEN oep_loss END))  AS oep_200,
       ROUND(MAX(CASE WHEN aep_rank = 50  THEN aep_loss END))  AS aep_200,
       ROUND(MAX(CASE WHEN oep_rank = 40  THEN oep_loss END))  AS oep_250,
       ROUND(MAX(CASE WHEN aep_rank = 40  THEN aep_loss END))  AS aep_250,
       -- TVaR: the mean of every year at or beyond the return period
       ROUND(AVG(CASE WHEN oep_rank <= 100 THEN oep_loss END)) AS tvar_oep_100,
       ROUND(AVG(CASE WHEN aep_rank <= 100 THEN aep_loss END)) AS tvar_aep_100,
       ROUND(AVG(CASE WHEN oep_rank <= 40  THEN oep_loss END)) AS tvar_oep_250,
       ROUND(AVG(CASE WHEN aep_rank <= 40  THEN aep_loss END)) AS tvar_aep_250,
       ROUND(MAX(aep_loss))                                    AS worst_year
FROM ranked r CROSS JOIN exposure x

One engine ran this one statement over those inputs and returned in 31 seconds:

Measure	Value
Buildings / footprint area	164,411 / 40,526,588 m²
Simulated years / events	10,000 / 10,003
Years with no loss	7,192
AAL	34,063 m²
1-in-10 AEP	46,912 m²

Return period	OEP PML	AEP PML	OEP TVaR	AEP TVaR
1-in-100 (rank 100)	752,284	754,615	1,385,983	1,420,802
1-in-200 (rank 50)	1,081,560	1,116,944
1-in-250 (rank 40)	1,324,438	1,338,751	2,055,859	2,111,891

First, OEP and AEP almost coincide at 1-in-100, 752,284 against 754,615 m². They stay close at 1-in-250, 1,324,438 against 1,338,751. With a Poisson mean of one event a year, few years hold a second large event, so the gap stays small. A peril with several damaging events a year, or with clustered arrivals, would pull the curves apart. Second, TVaR at 1-in-100 is 1,420,802 m², almost double the 754,615 PML. The 99 worse years carry much larger losses than the 100th. Third, the worst year, 6,678,861 m², comes from one footprint over the mainland. That 1-in-10,000 year sits far beyond either PML.

To draw the figures, the same named subqueries, called CTEs (common table expressions), feed two other final statements. SELECT sim_year, n_events, aep_loss, oep_loss, aep_rank, oep_rank FROM ranked returns the 10,000-row year loss table behind the curves. The map query lists the footprints of two years, a building count grid, and the county outline:

-- Same CTEs as above (centers also keeps s.lon and s.lat), then:
SELECT 'fp' AS kind, f.sim_year, f.event_id, f.lon, f.lat, f.radius_m, f.peak_dr,
       e.loss, CAST(NULL AS BIGINT) AS n, CAST(NULL AS STRING) AS wkt
FROM footprints f LEFT JOIN event_loss e ON f.event_id = e.event_id
WHERE f.sim_year IN (5588, 3471)
UNION ALL
SELECT /*+ BROADCAST(c) */ 'cell', NULL, NULL,
       FLOOR(ST_X(ST_Centroid(b.geometry)) / 0.006) * 0.006 + 0.003,
       FLOOR(ST_Y(ST_Centroid(b.geometry)) / 0.006) * 0.006 + 0.003,
       NULL, NULL, NULL, COUNT(*), NULL
FROM wherobots_open_data.overture_maps_foundation.buildings_building b, county c
WHERE b.bbox.xmin > -95.235 AND b.bbox.xmax < -94.369
  AND b.bbox.ymin > 29.083 AND b.bbox.ymax < 29.600
  AND ST_Intersects(c.g, ST_Centroid(b.geometry))
GROUP BY 4, 5
UNION ALL
SELECT 'county', NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
       ST_AsText(ST_SimplifyPreserveTopology(g, 0.002))
FROM county

Year 5588 has three events. One of them, with a 17.7 km radius, causes all 6,678,861 m² of its loss. Year 3471's four events sum to 2,443,060 m², eighth worst by AEP. Its largest event, 1,766,737 m², ranks 16th by OEP.

A production model swaps each toy part for a real one: a stochastic event catalog, hazard rasters joined with RS_ZonalStats, vulnerability curves by construction class, and policy terms. The SQL shape stays the same. The event-to-building join is the step that grows with the portfolio.

Research and what changes at scale

PML research grew from underwriting, hazard science, and simulation with risk measures, which met in the 1990s:

• Underwriting. McGuinness (1969) and Wilkinson (1982).
• Hazard. Gumbel (1941) and Cornell (1968), whose probabilistic seismic hazard analysis sets the 475-year ground motion in every SEL and SUL.
• Simulation and risk measures. Clark (1986), Grossi and Kunreuther (2005), Artzner et al. (1999), Acerbi and Tasche (2002), and Rockafellar and Uryasev (2002).

Open problems

• Tail estimates from finite catalogs. The 1-in-250 loss in a 10,000-year catalog rests on its 40 worst years, and TVaR at 1-in-250 averages those same 40. Both move when the catalog is resampled. A PML quoted without an interval does not show that spread.
• Secondary uncertainty. The damage ratio at a given wind speed is itself uncertain. Models that sample it widen the EP curve, and models that use its mean narrow the tail.
• Event clustering. AEP depends on how many events a year can bring. A Poisson count, as in the walkthrough, assumes independent arrivals. Mailier, Stephenson, Ferro, and Hodges showed in Serial clustering of extratropical cyclones (Monthly Weather Review, 2006) that European windstorms arrive in clusters. Clustered arrivals put more large events in the same year than a Poisson count does.
• Nonstationarity. A return period assumes a stable climate and a stable exposure. Coastal growth and warming seas change both. A 1-in-100 PML computed against today's buildings describes today's portfolio.

What scale changes

A national portfolio has millions of locations, and a stochastic catalog holds many thousands of events. The location-event spatial join is the largest step in the workflow. Jia Yu, Jinxuan Wu, and Mohamed Sarwat's GeoSpark (ACM SIGSPATIAL 2015) introduced spatially partitioned joins on Apache Spark. Yu, Zhang, and Sarwat's Spatial data management in Apache Spark: the GeoSpark perspective and beyond (GeoInformatica, 2019) describes the partitioning and indexing that became Apache Sedona. Sedona is the engine under WherobotsDB.

The models people use every day were trained on text, documents, databases, and the internet. Those sources cover the definition of PML. None of them holds the number of insured buildings inside last night's hurricane wind field from a weather model such as the High-Resolution Rapid Refresh (HRRR). An AI agent connected to exposure and hazard tables through the Wherobots Model Context Protocol (MCP) server can get that number with a spatial query.

Conclusions

The Galveston walkthrough shows that a portfolio PML is one point on an EP curve, and each finding below states what a PML figure needs beside it.

1. A PML needs its return period and its OEP or AEP basis. At 1-in-100, the toy OEP and AEP PMLs are 752,284 and 754,615 m². A Poisson mean of one event a year keeps them close. Perils with several events a year pull the curves apart, so a PML without both labels cannot be compared.
2. A PML understates the losses in the years beyond it. The 1-in-100 AEP TVaR, 1,420,802 m², is 1.9 times the PML. The worst year is 8.9 times it. Size capital from TVaR or the full year loss table.
3. AAL sets the expected-loss part of the premium, and PML sets the capital. AAL is 34,063 m² a year against a 1-in-250 AEP PML of 1,338,751 m², a 39-fold gap.
4. A PML from one catalog is an estimate. The 1-in-250 PML is the 40th worst of 10,000 years. Resample the catalog or report an interval before it sets a reinsurance limit.
5. A portfolio PML depends on the event-to-location join. 164,411 buildings against 10,003 events ran in 31 seconds as one SQL statement. A production catalog against millions of locations is the same join at a scale that needs a distributed engine.
6. For a clustered peril, the AEP PML sits farther above the OEP PML than this walkthrough shows. The toy assumes independent Poisson arrivals, and Mailier and colleagues found that European windstorms arrive in clusters.

Related terms

• Catastrophe modeling: the models that produce EP curves, AAL, and PML
• Stochastic modeling: simulating thousands of years of events
• Flood risk data: hazard layers joined to exposure
• Parcel data: property records behind each insured location
• Building footprint: the outline that places each insured building
• Spatial join: matching locations to hazard footprints
• Physical AI: AI that works with real places and the risks they face

Read more from Wherobots

• How to score every building in a state for catastrophe risk
• El Niño 2026, atmospheric rivers, and California's burn scars: one SQL engine, two data models
• Insurance use cases in the Wherobots docs

Join exposure to hazard layers with a Wherobots free trial at cloud.wherobots.com.