well as improved representation of hazards. Investment in research and technology in the field has been driven by the inadequacies of the historical record, mainly insurance claims data, for extreme events, and specifically by the inability of these data to robustly capture the statistics of catastrophic loss on insured portfolios. Unlike automotive or health claims, which are numerous and lend themselves to more reliable curve fitting for frequency and severity distributions, the small number of records of low-frequency and high-severity loss-making events do not provide sufficient evidence for such actuarial analysis. . While EP curves can be constructed from 20 years of observed historical loss data, they are limited to low-return-period estimation, are highly erratic and sensitive to data addition, and almost certainly underestimate loss levels, especially when considering average annual loss (Verisk 2013). Such records are rarely representative, especially in the extreme tail of the EP curve, which has few if any points to define it and is of primary importance to insurers and reinsurers. That is, history is not a good predictor of all possible future events.

Moreover, in low-income regions of the world, there is often acute data scarcity around historical evidence of natural hazards. The resulting short time series of hazards hampers the estimation of the EP curve. The increasing availability of remotely sensed weather information from satellites has helped provide global coverage for hazardrelated data sets that now range from 10 years to 40 years in length. The range of variables inferred from satellite data has also expanded to include new ones such as soil moisture, as new sensors come online and provide reliable training and validation data.

A key component of catastrophe modeling is developing statistical and physics-based methodologies, which vary by hazard type, to extend limited historical catalogs of events to many thousands of years of probabilistic events in order to adequately capture frequency, extreme severities, and full geographical location. This process is computationally intensive, and great care must be taken to ensure that resultant event sets are constrained by observed physical processes; for example, definition of hazard parameter distributions of climatological characteristics must maintain spatial and temporal correlations. Model calibration and validation against historical information are a valuable check, but inevitably assumptions are required on data processing and sampling steps, ideally supported by academic reference (ABI 2011). Though the event-by-event loss calculations of catastrophe modeling are computationally intensive, especially for hazards that demand high geographic resolution (which can be less than 10 m for flood), these calculations also allow differing aspects of model uncertainty to be quantified and communicated.<sup>7</sup> Only such a large time series of synthetic but nevertheless realistic events can generate enough samples of losses to robustly define the remote tail of EP curves that are of interest to the insurance industry, such as 1-in-100-year and 1-in-250-year return periods. Taking such a probabilistic loss perspective also ensures the EP is smoothed out by having many thousands of data points. For the purposes of this paper, a 10,000-year stochastic catalog of synthetic simulations was generated across Malawi at a spatial resolution of 0.05° and dekadal temporal resolution for several hazard variables (including soil moisture).<sup>8</sup> These 10,000 years of hazard events are all potential versions of what could happen in the next 12 months and can be combined with vulnerability and exposure information to estimate longer return period tail behaviors) to get a fuller risk perspective. This step requires making assumptions about the relationship between hazard and impact, using historical data as a starting point. In a data-scarce environment, it can be very hard to validate the performance of the vulnerability function in the tails. This paper is a starting point, and more investigation is required.

As noted above, these 10,000 years of hazard events reflect events that are likely to occur under current (and near-current) climate conditions, rather than forecasting climate conditions 100 years (for example) in the future. In this way catastrophe models differ significantly from general circulation models/global climate models (GCMs), 7 LMA (Lloyd’s Market Association), “Understanding Uncertainty in Catastrophe Modelling for Non-Catastrophe Modellers,” <u>https://www.lmalloyds.com/lma/readfile.aspx?iDocumentStorageKey=cc44f6be-b83f-4cf9-903ce802c1f312a8&iFileTypeCode=PDF&iFileName=Understanding%20uncertainty%20in%20cat%20modelling%20for% 20non-cat%20modellers.</u> 8 Given the computational requirements to generate such a stochastic catalog, this exercise was completed for only one country.

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