¹ Uninsured Losses, report for the Tsunami Consortium, November 2000.

² See, for example, http://environmentalchemistry.com/yogi/environmental/asbestoshistory2004.html

³ A copula is a functional, whose unique existence is guaranteed from Sklar’s theorem, which says that a multivariate probability distribution can be represented uniquely by a functional of the marginal probability functions.

⁴ Applied insurance research (AIR), for example, stochastically samples the damage for each event on each property and the simulation is for a series of years. Risk management solutions (RMS), on the other hand, take each event as independent, described by a Poisson arrival rate and treat the range of damage as a parameterized beta function (’secondary uncertainty’) in order to come up with the OEP curve, and then some fancy mathematics for the AEP curve. The AIR method is the more general and conceptually the simplest, as it allows for non-independence of events in the construction of the events hitting a given year, and has built-in damage variability (the so-called secondary uncertainty).