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On Complex Economic Dynamics: Agent-Based Computational Modeling and Beyond Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Is Risk Quantifiable?

Authors : Sami Al-Suwailem, Francisco A. Doria, Mahmoud Kamel

Published in: Complex Systems Modeling and Simulation in Economics and Finance

Publisher: Springer International Publishing

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Abstract

The work of Gödel and Turing, among others, shows that there are fundamental limits to the possibility of formal quantification of natural and social phenomena. Both our knowledge and our ignorance are, to a large extent, not amenable to quantification. Disregard of these limits in the economic sphere might lead to underestimation of risk and, consequently, to excessive risk-taking. If so, this would expose markets to undue instability and turbulence. One major lesson of the Global Financial Crisis, therefore, is to reform economic methodology to expand beyond formal reasoning.

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previous chapter Supercomputer Technologies in Social Sciences: Existing Experience and Future Perspectives
Footnotes
1
But see Sect. 3 below.
 
2
We will later elaborate on that characterization.
 
3
We use here “model” in the sense of “mathematical model”, that is, the mathematical depiction of some phenomenon; we do not use it in the model-theoretic sense.
 
4
That is, the set of theorems of S is recursively enumerable.
 
5
This is what we mean by “enough arithmetic”. Actually we can obtain the same results we require if we add a still weaker arithmetic condition.
 
6
The theorem that implies such a result is a Rice-like theorem proved by da Costa and Doria in theorem 1990; see Chaitin et al. [28].
 
7
A simple proof can be found in Chaitin et al. [28].
 
8
Yet the Arrow–Debreu theory is undecidable; that follows from a theorem by Tsuji et al. [107].
 
9
For a summary discussion, see http://​http://​www.​fattails.​ca.
 
10
Personal communication to FAD.
 
11
In binary form, zeros and ones are evenly distributed.
 
12
Actually an injunction engraved at the Apollonic oracle at Delphos.
 
13
Yet one must be careful here, as the so-called “reflection principles” may be interpreted as sentences of the form “X is true”.
 
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Metadata
Title
Is Risk Quantifiable?
Authors
Sami Al-Suwailem
Francisco A. Doria
Mahmoud Kamel
Copyright Year
2018
Book
Complex Systems Modeling and Simulation in Economics and Finance

Print ISBN: 978-3-319-99622-6

Electronic ISBN: 978-3-319-99624-0

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-99624-0_14