A decision theoretic tool for the North Atlantic Hurricane Season
Leveraging the confidence approach to make transparent
insurance decisions under uncertainty
Welcome to our web-based tool that aims to open a discussion on the use of decision-theory based frameworks in catastrophe risk modelling and management.
The project was spearheaded by Maximum Information and the London School of Economics and Political Science with funding provided by the Lighthill Risk Network .
It is stressed that this is an experimental tool designed for research purposes; we accept no liability for any real-world decisions made using the tool.
What is the idea behind this tool?
The tool leans on the decision theoretic confidence approach Hill [2013] , Bradley [2017] to construct a practical framework for:- Transparently reflecting the outputs of an ensemble (i.e. a number) of predictive models
- Efficiently and defensibly collapsing the output ensembles based upon decision-relevant attitudes of decision-makers.
Why is this relevant for natural catastrophe risk?
Catastrophe risk is, almost by definition, subject to severe and complex uncertainty. In contemporary cat modelling frameworks, it is often impossible for decision-makers to justify the personal reasoning behind specific catastrophe risk management decisions. This is because the uncertainty in the modelling has been pre-collapsed for them by frameworks that aim to make the decision-making process more efficient, and provide in advance 'objective' best estimates out of the ensemble (e.g., a single number representing an average expected loss of all model runs).It is debatable whether the term 'objective' is at all meaningful for uncertainties that are as wide as they are in catastrophe risk management. Regardless, at a minimum this adherence to objective best estimates leaves decision-makers at risk of severely misjudging the magnitude of uncertainty, while also introducing a systemic (and incorrect) assumption that all stakeholders have the same tolerances to risk and volatility.
By introducing separate 'stakes' and 'cautiousness' levers, the confidence approach framework provided here allows users with a wide variety of risk tolerances to defensibly define their preferences without losing efficiency.
What is the case study used in this tool?
Here, we assume a capital provider is choosing whether or not to underwrite a simple parametric insurance cover with a binary payout. The cover pays out when a hurricane of Cat 1 (or Cat 3) intensity or greater makes landfall in the North Atlantic basin. There is no limit to the number of times the cover can pay losses in a given year if there are multiple landfalls.The tool allows the user to examine how their approach would fare in historical years, as well as offer a 'live' example based on 2026 forecasts of hurricane activity.
General Information
Forecasts for previous years were selected for the purposes of demonstrating the approach ('Backtest') and for the current year 2026 ('Forecast'). For this example we assume there is a binary payout in the case of either a Category 1+ event or Category 3+ event.
Inputs Selection
In this section, you can set the key inputs for the parametric insurance cover.
- Year of interest: backtest years from 2017 to 2025, or the 2026 forecast.
- Intensity category: Hurricane intensity, i.e. Cat 1+, or Major Hurricane intensity, i.e. Cat 3+.
- Forecast release period: following the Seasonal Hurricane Predictions releases, i.e. March–April, May–June, or July–August.
The forecasts refer to hurricane activity across the North Atlantic basin. To translate this into landfall activity, the user can select an activity-to-landfall conversion factor. The midpoint of the slider is based on the North Atlantic basin landfall-to-activity ratio estimated from IBTrACS data for 1980–2025.
These selections feed into the tables below.
The 'Historical Climatology Rates' plot in this section shows the rates derived from the historical data (climatology) for the period 1900-2025. Each dot on this plot represents a specific segmentation of the historical data based on a given scientific narrative, such as the ENSO phase, giving eight views in total. More detail on the different climatological views used for this analysis can be found in the Reference tab.
The 'Seasonal Forecast Rates' plot in this section instead shows rates derived from forecasts compiled by the Seasonal Hurricane Predictions platform, led by the Barcelona Supercomputing Center. Each of the dots on this plot represents a separate entity's forecast. More detail on the seasonal forecasts used for this analysis can be found in the Reference tab.
Decision Information
Stake corresponds to the significance of the possible loss, with 1 being equivalent to exposing the insurer to ruin in the case of loss being sustained and 0 being a decision that is completely immaterial for profitability/capital considerations. Higher stakes require greater confidence before acting.
Cautiousness corresponds to the level of certainty required given the amount at stake, and can be thought of as a way of mapping risk appetite to different levels of potential exposure. In this section you define where on the stakes slider you would need low, medium and high confidence. The blue middle section represents the area of medium confidence with the grey sections on either side representing low and high confidence. Further detail can be found in the Reference tab.
The overlay between stakes and cautiousness determines the level of confidence required for your decision.
Pricing Information
Select the payout for the cover and the market (or Firm Order Terms) premium the capital provider will receive for writing the cover. The capital provider is assumed to be a price-taker, with no real ability to influence the market or FOT premium. The slider can be thought of as representing different stages of the insurance cycle. The default value is based on the historical long-term rate, loaded by 20%, and is intended solely for illustrative purposes.
View From IBTrACS Climatology
This view uses the rates derived from the historical data (climatology). The historical data is segmented based on different scientific narratives (e.g., ENSO phase), giving a number of different views. More detail on the different views used for this analysis can be found in the Reference tab.
View From Seasonal Forecasts From Seasonal Hurricane Predictions
This view uses the seasonal forecast data compiled by the Seasonal Hurricane Predictions platform. The rates are derived from a number of credible seasonal forecasts released in advance of the North Atlantic hurricane season. See the Reference tab for more detail on the seasonal forecasts used.
Methodology
Where does the framework come from?
The framework stems from foundational catastrophe risk challenges presented to Profs. Roman Frigg and Richard Bradley by Tom Philp starting in 2016. This led to the development of a theoretical hurricane problem and, subsequently, to the publication of the peer-reviewed paper 'Making Confident Decisions with Model Ensembles' by Joe Roussos, Roman Frigg and Richard Bradley.
The practical framework presented on this page is the first attempt to make the theoretical framework from that foundational paper practicable.
Where does the data come from?
The tool ingests external Tropical Cyclone data. The raw historical data is available from the International Best Track Archive for Climate Stewardship (IBTrACS). From these data, we derive a set of climatologies representing different scientific narratives.
Each climatology is based on a subset of the IBTrACS dataset:
- Long-Term Rate (LTR), 1900–2025: historical activity over the period considered accurate for estimating long-term landfall rates.
- 10-Year Persistence: historical activity over the most recent 10 years.
- 20-Year Persistence: historical activity over the most recent 20 years.
- AMO Positive: historical activity during the warm phase of the Atlantic Multidecadal Oscillation.
- AMO Negative: historical activity during the negative phase of the Atlantic Multidecadal Oscillation.
- ENSO – El Niño Years: historical years in which the season was in an El Niño phase.
- ENSO – Neutral Years: historical years in which the season was in a neutral phase.
- ENSO – La Niña Years: historical years in which the season was in a La Niña phase.
Seasonal prediction data for 2026 and previous years are derived from the Seasonal Hurricane Predictions platform, which collates credible seasonal forecasts issued by a number of universities, private sector entities and government agencies around the world for the upcoming hurricane season in the North Atlantic. The platform has been co-developed by the Barcelona Supercomputing Center and Colorado State University, in partnership with AXA XL.
Is this a hazard- or loss-focused tool?
While the output is shown as losses, it should be stressed that the tool makes a simple binary parametric-payout leap from a Cat 1+ or Cat3+ landfall to total loss. At present, this is therefore a hazard-focused tool, with loss figures provided primarily to help users connect conceptually with how the framework can be used in catastrophe risk management.
What is coarse-graining?
Coarse-graining is the process of dividing model predictions, in this case annual hurricane landfall rates, into different ranges according to the level of confidence required for the decision. In our framework, these ranges are referred to as low, medium and high confidence. This is done by ranking the model predictions by their distance from the median estimate. The closest third of model estimates to the median represents the low-confidence range; the closest two-thirds represent the medium-confidence range; and the high-confidence range includes all model estimates.
The 'confidence adjusted' view in the results section takes the upper bound of each range to calculate the technical premium. By coarse-graining the cautiousness levels, as in Roussos et al. (2021), and overlaying them with the stakes information, we obtain the upper bound of the ensemble that is most appropriate for the risk. This then provides a recommendation for pricing the risk, leaving aside acquisition expenses, operating expenses and capital loading considerations.
Glossary
Event Rate: The average annual frequency or rate for the given approach across all relevant models.
Adjustment vs LTR: The extra margin over the event rate required to write the risk, expressed as a percentage of the IBTrACS LTR event rate.
Forecast Error: The difference between the projected event rate and the actual event rate that transpired during the year in question. A positive sign indicates an overestimate and a negative sign an underestimate.
Technical Premium: The suggested premium charged for the cover based on the selected approach. This is the Event Rate x Max Payout. Where we are using the confidence-loaded approach, this additional confidence load must be taken into account: Technical Premium = Event Rate × (1 + Confidence Load) × Max Payout E.g., if the Event Rate is 0.2, the Max Payout from an event is $1m and the Confidence Load is 10%, then the capital provider would need to be paid at least 0.2 x ( 1 + 10%) x $1m = $220k to write the risk. We ignore cost of capital/expenses here so this is not factored into the calculation.
Underwriting Decision: The decision taken by the capital provider as to whether to use their capital to write the cover in question. There are only two outcomes here, 'Write Risk' or 'Don't Write Risk'. It is assumed the capital provider writes the risk if they receive at least the Technical Premium calculated under the approach, and otherwise does not write it.
Return: The return the capital provider would receive after receiving the market premium and paying any losses. If losses occur during the year and they have chosen to write the risk, then these are deducted from the premium to give the overall return. If they do not write the risk, then the return is simply zero.
Market Premium: The actual premium determined by the broker/client. This is selected by the user and can be adjusted using the slider to give a rough idea of how this might vary with the market cycle. The default and middle of the slider is set to the Long Term Rate (LTR) average rate from the IBTrACS (historical) data multiplied by the Max Payout with a 20% margin. This is an arbitrary selection and is not meant to be reflective of actual market conditions.
Market Implied Rate: The landfall rate implied by the market premium. Corresponds to Market Premium / Max Payout.
Actual Event Rate: The actual landfall rate during the season, in this case how many Cat1+ (or Cat3+) hurricanes made landfall in the North Atlantic basin during the season in question.