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Hi everyone! My name is Lauren and I’m a current senior. I will be presenting next Wednesday, March 17 at 2:10. For a brief introduction to what I will be talking about, consider the following hypothetical situation:

Let’s consider the students at Canisius College, and assume there are 2,000 students with an average height of 5.5 ft. If Canisius College begins an foreign exchange program with a distant alien planet, there could potentially (ridiculousness aside) be an alien student at Canisius College that is two miles tall. With the inclusion of this one student in the height statistics, the new average height of Canisius students is about ten feet and nine inches. Is this unreasonable? You would then anticipate an outsider of Canisius College to look around campus and see every student to be about ten feet and nine inches. This outsider would be disappointed (or relieved) to look and see this is not the case. So the question becomes should this new student be included in the average height data if their height qualifies them as an outlier? Likely, the answer is no, for logical reasons. By contrast, consider a major financial corporation, and the new student two miles tall represents an unexpected, unexplainable event that has the potential to drain company assets and bankrupt it. Financial analysts would want to consider the possibility of something like this occurring because of the significant impacts that it would pose. Events that are unlikely, but not impossible, can still occur.

My presentation will focus on extreme events and the types of probability distributions that we would be better off predicting extremes with: stable distributions. An introduction to the types of stable distributions, and then specifically the Cauchy distribution will be made. Applications of these distributions will be shown through R-Studio output of financial data, which will serve as a visual of a Black Swan event. A majority of this presentation will pull from the work of Dr. Nassim Nicholas Taleb, who has devoted his post-financial industry life to mathematical philosophy applied to probability and randomness. It is beneficial to have taken Probability and Statistics 1 & 2, but not a requirement, as some basics will be explained.

A special thank you to Dr. Leonid Khinkis, whose advice and knowledge of these fields has been extremely helpful in guiding me though this work.