Investigating the threshold of event detection with application to earthquake and operational risk theory

Abstract

This study provides systematic analysis of points of structural change in probability distributions. In observed frequency data of earthquakes, such a threshold exists due to the non-detection of events below a certain magnitude. By examining the factors in uencing the operational risk exposure of institutions, a similar threshold is hypothesized to exist in operational loss data. In both elds of study, this threshold is termed the threshold of completeness, above which 100% of events are de- tected. External factors have caused this level of completeness to shift over time for earthquake data. The level of complete recording in uences the volume of data that can be consistently incorporated in a study of seismic activity. Such data can be used by re-insurers and direct writers of catastrophe agreements who deal in seismic hazard. Historically, a variety of methods have been proposed by authors in an attempt to gauge the location of the threshold of completeness in earthquake data. This study aims to evaluate the e cacy of some of the most prominent methods under di ering assumptions regarding the incomplete portion of the data. Furthermore, a new threshold estimation scheme (MITC) is developed and tested against the prevailing methods. Additionally, earthquake data and the wealth of literature will aid in introductory analysis and assessing applicability of esti- mation techniques in the context of operational losses.