The Modelling of Extreme Events

Abstract

The modelling of extreme events is becoming of increased importance to actuaries. This paper outlines the various theories. It outlines the consistent theory underlying many of the differing approaches and gives examples of the analysis of models. A review of non-standard extreme events is given, and issues of public policy are outlined.

Longevity bond premiums: The extreme value approach and risk cubic pricing

“…The key idea in the EVT is to ''estimate extreme probabilities by fitting a model to the empirical survival function of a set of data using only the extreme event data rather than all the data, thereby fitting the tail, and only the tail'' (Sanders, 2005). In this sense, the advantage of the EVT approach can also be viewed as a disadvantage: it focuses on the tail distribution and ignores the central regions of the data.…”

“…On the other hand, we need to keep u low so that we have enough data to estimate the parameters (control the variance). A typical choice of u is around the 90th to 95th percentile (Sanders, 2005).…”

“…In Section 4, we model the mortality dynamics using a random walk with 2 Embrechts et al (2008) and Reiss and Thomas (2001) provide detailed discussions of EVT and its application to insurance and finance. See also Mikosch (1997), McNeil (1997), McNeil and Frey (2000), Kotz and Nadarajah (2000), and Sanders (2003Sanders ( , 2005.…”

Catastrophic oil spill analysis

“…In recent years, statistical theory of extreme values, especially the extreme value theory (EVT), have been widely used in studying rare events, including hurricane damage, stock market crash, insurance claim, flooding, earthquake, sea level rise, etc. [2][3][4]. In this paper, the EVT is applied to analyze oil spills in the U.S. outer continental shelf (OCS) in the past 49 years .…”

“…It provides models relevant for the assessment of rare events, even outside the range of previous observations. Extreme value methodology is now commonly used in a wide range of fields, such as economic damage [7,8], finance [2,3], earth sciences [4,9,10], traffic prediction [11], large oil spills [12], etc. This paper focuses on how the statistical theory of extreme values can be applied to improve the oil spill risk analysis.…”