Saturday, March 10, 2018

"Why Black Swan events must occur - an ontological investigation"

I assume by their use of the lowercase "g" in "god" in the first paragraph of the introduction the authors are referring to Taleb himself in the pantheon of lifters.

From>Quantitative Finance>Risk Management, March 7:
We develop a first-order deductive system to show that the occurrence of Black Swan events is implied by their definition. It follows as a corollary of our theorem that any computational model of decision-making under uncertainty is incomplete in the sense that not all events that occur can be taken into account. In the context of decision theory we argue that this constitutes a stronger sense of uncertainty than Knightian uncertainty.
1. Introduction 
Ontology, loosely defined as ” the study of what there is ” (Hofweber, 2014), studies questions of the existence of entities, their properties, and the relation between the two (Hofweber, 2014). So-called ontological arguments traditionally are proofs of the existence of god, deducing this conclusion from a set of properties attributed to the entity ‘god’ . In this article we apply the same technique to show the existence of so-called Black Swan events.

The notion of Black Swan events, originally introduced in Taleb ( 2005 ), has been popularized by a series of popular science books ( Taleb , 2016 ). Its formalization is work in progress by Taleb (2017). Their naming makes reference to the so-called problem of induction , defined by the Oxford English Dictionary as ” the process of inferring a general law or principle from the observation of particular instances ” (OED, 2017). As first discussed by David Hume, such arguments cannot be m ade rigorous by deductive reasoning alone, given the lack for a justification of the assumption that yet unobserved entities will share the same properties as those already observed (Hume and Selby-Bigge, 1896). The solution to the problem that this causes to scientific reasoning proposed by Popper (1935 ) is to replace induction with falsification, the process of continuously trying to find empirical evidence against the theses of a scientific theory (Vickers, 2016).

It was long believed, especially before the enlightenment, that inductive reasoning was a valid form of drawing conclusions. A common way of presenting this argument was to claim that it could be concluded from the fact that all swans observed hitherto (in Europe) we re white that indeed all swans were white. For this reason, the discovery of a species of black swans in Australia – cygnusatratus – during the voyages of the 17th century, first recorded by the Dutch skipper Antony Caen in 1636 and confirmed over 60 years later by Willem de Vlamingh (Olsen , 2001), was truly shocking to European thinkers, as it undermined the very logic of inductive reasoning. The combination of the rarity of such sightings and their relatively high impact (the questioning of an entire school of thought) was likely what led Taleb ( 2016 ) to choose cygnus atratus as the namesake for events with these properties

The theory of Black Swan events, under development by Taleb (2017), has already made a significant impact in popular language and general media. In this articl e we undertake to demonstrate that the occurrence of such events is in fact implied by their definiti on. Several authors have written about Black Swan events from a statistical and risk (management) theory perspective. Taleb (2005); Yudkowsky ( 2008 ) discuss Black Swans in the context of human cognition and it's limitations. However, there are – to the best of our knowledge – no works looking at Black Swans from an analytical perspective....
....MUCH MORE (18 page PDF)

Cornell University Library download page.