_n_ is the total number of CSs; _j_ is hurricane intensity given as Saffir-Simpson category 1 to 5.

W _i_ is the property value in the _i_<sup>th</sup> CS; H _i,j_ is the annual probability of occurrence of a hurricane of intensity _j_ in the _i_<sup>th</sup> CS; and D _j_ is the portion of property value lost to hurricane of intensity _j_ .

W _i_ can be described as an _exposure distribution_ ; H _i,j_ a _hazard distribution_ , and D _j_ a _damage function_ . These three elements of a catastrophe model determine annual probability of losses to property. The model underlying (2) above is highly simplified in many respects—for one, it assumes one hurricane, no more and no less, per year. The details of full blown catastrophe model are difficult to summarize into a simple model like this, but to give the reader a general feel for rough numbers, for major hurricanes (j=3,4,5), D _j_ is roughly 10 percent for insured losses. In a major coastal segment of property, such as around Miami, Florida, total property value, W _i_ (where i is suitably chosen to select the coastal segment that encompasses the greater Miami area), is effectively around 1 trillion USD<sup>1011</sup> . Therefore, given these simplified numbers, a major hurricane striking a major urban coastal segment of property is expected to cause an insured loss of property of about 100 billion USD. Such an event (major hurricane striking a major urban coastal segment of property) is expected to occur with annual probability of about 1 percent, or once every 100 years.<sup>12</sup> Therefore, as of 2009 we would say that a 1-in-100 year hurricane insured loss is 100 billion USD. The hazard distribution is considered relatively stable and biased toward higher intensity storms in warmer, southern waters<sup>13</sup> . In an unfortunate, partial coincidence, the US East Coast exposure distribution is sometimes, though not always, peaked where the coastline juts out into the ocean as well<sup>14</sup> . The damage function is relatively stable over time, so the main factor affecting changes in hurricane risk is changes in the exposure distribution. For US hurricane, AAL is currently estimated at about 10 billion USD<sup>15</sup> .

Catastrophe models use Monte Carlo techniques to generate 10 thousand years or more of simulated losses. Using the simple model above, a catastrophe model would generate random occurrence of hurricanes in simulated year via H _i,j_ , then overlays those random hurricanes on the fixed property distribution, W _i_ . The damage function D _j_ then translates the incidence of 10 FHCF website.

11 These figures are very high in absolute terms, and represent about 7 percent of the 2008 US GDP. Hurricanes hitting small islands can losses that are several times larger than their GDP. For example, a major hurricane hitting Jamaica could cause losses of more than 200% of GDP.

12 Note again that these numbers are rough and not consistently defined from researcher to researcher. For example, depending on how strictly one defines a hurricane strike on a particular location (from landfall within 5 miles to bypassing within 90 miles), the probability of a strike on a particular location can vary by a factor of 10 from model to model. Here, an emphasis was placed on giving round numbers that bear a reasonable resemblance to the kinds of numbers used in detailed commercial catastrophe models.

13National Hurricane Center website. See in particular the Climatology section. http://www.nhc.noaa.gov/HAW2/english/basics.shtml

> 14 Pielke, Jr., R. A., Gratz, J., Landsea, C. W., Collins, D., Saunders, M. A., and R. Musulin (2008): “Normalized Hurricane Damages in the United States: 1900-2005,” _Natural Hazards Review_ , vol. 9, no. 1, pp. 29-42.

http://sciencepolicy.colorado.edu/publications/special/normalized_hurricane_damages.html 15 Karen Clark & Company (2008): “Near Term Hurricane Models: How Have They Performed?” http://www.karenclarkandco.com/pdf/KCC_NearTermHurricanes.pdf 5