Between 2006-2011 I was the "RCUK Academic Fellow" in Financial Mathematics. In this role I was obliged to discuss my field with public and policy makers. Usually this "public engagement" aspect of the Fellowship was ignored, but the role of mathematics in finance became one aspect of the Financial Crises, the dominant theme of public discussion since the summer of 2007 and I was catapulted out of my comfort zone in mathematics.
The issue I really needed to address in discussion with outsiders was whether the involvement of mathematicians in finance was moral. Mathematicians do not like addressing issues of morality, and the standard response in the UK is to resort to G.H. Hardy's "claim" that a mathematician does nothing useful: mathematics is so irrelevant to society that it is morally neutral. I don't think this is (morally) acceptable for a whole load of reasons and so I had to address the substantive issue.
Since 2008 a substantial portion of my time has been spent on this problem, to the detriment of my mathematical research. However, it has had some impact. In 2011 the RCUK (the UK equivalent of the US National Science Foundation) recognised the result of this work as one of "One Hundred Big Ideas for the Future".
The "big" idea is that ethics have been central to finance, and out of the ethical examination of finance, mathematical probability emerged. This is a heterodox, but not unique, interpretation of the history of science. The significance of this is that modern mathematical approaches to derivative pricing implicitly involve the principle of reciprocity, which is anterior to the concept of justice and fairness and at odds with the orthodox objective of utility maximisation. This led me to address the issue as to why, today, we do not associate finance with ethics, and I came to the conclusion that during the first half of the nineteenth century, the Romantic period during which contemporary science was laid down, there were paradigm shifts in society comparable to those in the late seventeenth century. Specifically, in response to perceived scarcity, ideals of reciprocity were replaced by concepts of individuality and competition. By the 1950s the ideal of "my word is my bond" had been lost (see Buttle v Saunders).
I have drafted my argument in a paper available on SSRN (or ArXiv). The paper discusses the Fundamental Theorem of Asset Pricing within the context of measure theoretic probability, as opposed to Knightian or Keynesian conceptions of probability. It then discusses the Scholastic concept of the Just Price in the context of the genesis of probability. The importance of finance in the mathematisation of Western science is discussed as a prelude to the early development of mathematical probability in the context of the ethical evaluation of commercial contracts. This part finishes with an explanation of why the Fundamental Theorem appears equivalent to seventeenth century approaches to pricing assets.
The second part of the paper presents a narrative of why this equivalence is no longer obvious, arguing that neoclassical economics has been developed to address scarcity, where as the Fundamental Theorem addresses uncertainty. The paper finishes with some implications and considers the legitimacy of gambling, within the context of Virtue Ethics.
I am interested to hear any comments on this argument.
The implications of the argument, I believe, are very positive for economics. Firstly is the point that economics and social science is anterior/senior to the physical sciences. Historically the solution of economic problems precedes the solution of physical problems. An aspect of the contemporary situation is that economics relies on technology developed in the physical sciences, and is therefore inadequate. Recognising the seniority of social sciences can correct this situation. Secondly, there is an implicit implication that developing a better understanding of finance can have a positive impact on science as a whole. A significant issue in scientific debate is that data is rarely disputed, at the root of debates on, say climate change, GMOs etc, is disagreement on models. This is at the heart of modern finance (as discussed in the paper). Understanding how finance uses mathematics as a "rhetorical tool" can help everyone.
I am wary of the sectarian divisions in economics, but I feel my thesis leans heavily towards certain aspects of Post-Keynsian thought, specifically relating to the non-neutrality of money and having to deal with ontological uncertainty. More broadly, I think the paper is a clear argument against the fact/value dichotomy in economics and is aligned with McCloskey's project promoting virtue ethics within economics.
I hope the thesis sits within Pielke's "honest broker" classification. The thesis is an apologia for the use of mathematics in finance, which includes an argument legitimising speculation, suggestin advocacy. However it also provides a framework, in the context of virtue ethics, for when speculation is legitimate. I believe it contributes to being an "honest broker" in that it opens the debate and recognises that science is implicitly based on values, and if we are to get finance right we need to examine the normative basis on which we work.