Analysis of tropical storm damage using buffered probability of exceedance

Abstract

This paper explains the new concept of buffered probability of exceedance (bPOE). Through averaging of data in the tail, bPOE compactly presents probability as well as loss value of the tail and has the capability to revolutionize the concept of risk-averse engineering. bPOE is demonstrated using tropical storm damage along the Atlantic and Gulf of Mexico coasts of the USA from 1900 to 2013 (average yearly damage $14.776 billion). It can be shown, under general assumptions, that bPOE is more than double the probability of exceedance (POE). For instance, with a $50 billion threshold of damages per year, POE is 10.6 %, while the bPOE is 26.1 %. We also considered expected excess (EE) over some threshold (deductible), which is a minimum premium that insurer should charge per year. We demonstrate that EE equals the difference between the damage associated with POE and bPOE multiplied by bPOE. For instance, for a 25 % tail probability, the value at risk (quantile) determined using POE is $11.181 billion, while the conditional value at risk (average damage in excess of the quantile) determined by the bPOE is $51.753 billion. This $40.572 difference leads to EE of 0.25 * $40.572 = $10.143 billion over the threshold $11.181 billion. Furthermore, subdividing the data by landfall state, at the 50 % probability level, Florida, the state most often hit by tropical storms also has the highest value for EE at $8.111 billion; thus, quantifying the need for insurers to charge Floridians high insurance premiums.