The (un)rational Use of Mathematic in Finance

A Critical View on (Un)Rational Mathematic in Economy and Finance

In economics and finance, mathematical models are used to predict or evaluate events. This paper aims to outline the uncritical use of these quantitative systems, focusing on forecasts in finance and economics from an epistemological, ontological, and practical view. Forecasts are mathematical probabilistic predictions about future events, which are crucial drivers of the decision making process. Notably in financial markets, forecasts have dramatic impacts on stock-, business-, and investment valuations. Probabilistic models count the number of possible events and compare its frequencies in order to derive presumptions of how likely an event occurs. The central problem of forecasts is its incoherency when the observation set contains infinite possibilities of events. Considering the significance of these dynamic systems, imperfections can lead to devastating consequences for entire markets, making probabilities a poison pill. (Andersen et al. 2013)

Forecasts are subjective perceptions of the observer’s view about how certain events develop. The fact that financial mathematics cannot predict reality due to its complexity is contradicting with the rationality of mathematics.  It is more an abstract perspective on models, which provide oversimplified knowledge about the future. Ramsey (1931) underlines the subjective view on probability by seeing it as the logic of partial belief. Meaning, that forecasts are rather rational beliefs than objective relations, which defines it as a semantic model based on quantitative and syntactic factors. The knowledge that is derived from these dynamic models is a subject to prior knowledge of the observer, which underlines Knight’s approach that probabilistic uncertainty in mathematical forecasts is an epistemological problem. (Johnson 2012)

In turn, Platonism suggests viewing all kinds of mathematics from a metaphysical view, whose existence is independent of languages, knowledge, and practices. (Balaguer 1998) It is the reality of nature that two apples plus two apples are in total 4 apples, regardless of prior experience and knowledge. Referring this to probabilistic forecast models in economics and finance, it is more reasonable to apply Keynes’ approach, which suggests the nonexistence of mathematical probability of future events. (Johnson 2012) This ontological problem refers to the impossibility to consider the infinite set of possible events as well as to predict human behaviour using mathematical models.

Algorithmic systems used to calculate forward looking stock pricing models in investment banks are so complex that neither traders nor stockholders are able to interpret the systematic outcomes. The mathematical imperfection and the resulting error in the human ability to act rational was the reason for a 75% stock plunge of United Airlines in 2008. The algorithmic systems (Blackboxes) of investment banks recognized an increasing Google search of the airline name in combination with the word ‘bankruptcy’ and suggested traders to sell UAL stocks, leading to a 33% drop of the stock price within five minutes. (Ahrens 2008) However, there was no rational and logic reason for shareholders to sell their stocks but they did so because the algorithms commanded it. This caused a dramatic loss for UAL and highlighted major deficiencies in mathematical trading models.