Wednesday 24 October 2012

Ethics and Finance: The Role of Mathematics

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.


  1. Tim, I come at your issues from a Russell/Whitehead perspective, and have not (yet?) made the effort to understand your own starting point or approach, but your paper does seem very important.

    As against Hardy, it seems to me that a principled use of mathematics - such as yours - can uncover ethical issues and can at least be part of a critique on attempts to resolve them. When you say that finance has 'used' mathematics, there are two senses of the term. Firstly, it uses maths a means to its declared ends (making money). But it also uses maths to provide a cloak of respectability; 'this is mathematical, hence correct'.

    Your new theory mimics the development of the orthodox theory almost step by step, and hence is equally well clothed mathematically. It also has the merit of being produced by someone with your position and reputation (not unimportant). It thus - hopefully - removes the false cloak of mathematical inevitability from the orthodox theory, opening our eyes to some of the ethical choices available. (Something that Keynes failed to do.)

    It seems to me that this is just the sort of thing that policy makers need to understand if we are to sustain 'the good life' on anything approximating the current scale. But it isn't the only piece of the jig-saw.

    I hope to blog on this, just as soon as I think a way of framing my thoughts. I would be happy to hear from you. Best wishes. Dave Marsay

  2. I have come to my conclusions from the starting point that the financial markets are important beyond their ability to generate cash, and that mathematics is essential to understanding them.

    From this point, I learnt of the historically close relationship between finance and mathematics and the impact on western science (usury/FX -> Fibonacci -> Merton calculators -> Copernicus, Cardano, Stevin -> Descartes, Newton...) and how similar medieval finance was to contemporary finance (Asset Backed Securities = Censii, CDOs produced by the Fuggers, CDS in the Triple Contract).

    But, if you agree with the FCIC and the crisis of 2007-2009 was caused by a breakdown in ethics, if maths is going to be part of the solution it needs to offer an ethical fix. Because I think finance and maths are important, and I think the FCIC report was amongst the most thoughtful assessments of the crisis, I synthesised what I had learnt into an ethical argument.

    Another aspect is that I see the importance of maths in finance not in terms of producing "the" model, but is enabling discussion about competing models and the limitations of models. I think Gillian Tett's tale of J.P. Morgan in this respect is very important. But it goes beyond finance, the climate change debate is not about "facts" but "models" applied to the facts, so how maths and finance interact today is still relevant to how we understand science. It also emphasises the status of maths as a tool to understand rather than a tool to calculate.

    Related to this is the issue that "hidden science" is magic, and modern finance seems to want to operate behind a viel. I think this is the most pernicious aspect. I adhere to the believe that North West Europe was successful since the seventeenth century because there has been open, pluralistic debate, not because of our genes (Galton) or religion (Weber).

    I am keen to here comments, and have been invited to discuss the paper with social scientists at Edinburgh and I hear the Oxford PhD students are reading the paper as well. Get in touch directly if you want to discuss further.

    Are you going to come to the IMA Conference on Mathematics in Finance?

    1. Tim, I agree with your starting point and conclusions, but ...

      * The reference to ethics seems to me a distraction.
      * I would make a distinction between the use of off-the-shelf models and modelling. When faced with a potential crisis, one needs the latter.

      I was at a resilience conference last week. Many speakers emphasised the need for mathematics, but seemed to limit it to quantitative matters. I had a brief 'go' at Andrew Haldane afterwards and he seemed to take my points, which were much the same as yours. But where next?

      Your conference is attractive, not least because it is in Edinburgh. I may yet put in an abstract, based on my previous work. But I have had two problems:
      * I am not clear what the underlying problems are - I do not want to just treat symptoms. (Unethical!)
      * My impression of financial maths in general and your conference invitation in particular has been that it is looking for something more 'algorithmic' than I (or Keynes) would think was appropriate.

      I shall give it some thought. Regards.

  3. Tim, you are starting from a different place from me, but I think I get it, and it is important, and hopefully timely.

    You mirror the orthodox theory to develop a theory that is as respectable mathematically, but with very different policy implications, thus giving the lie to the default view that since the orthodox theory is supported by mathematics, it must be correct. Coming from you, I would hope that policy-makers would take this seriously.

    I need to get my own thoughts straight on this topic and blog myself. I would be happy to discuss.

  4. Interesting thoughts, Tim. Your method of framing the debate reminds me of a talk I heard about how the economics during the time of Christ informed Christian morality. In a world with under 1% growth, the majority of population semi-enslaved, there was good reason to eye the accumulation of wealth, and charging interest, with suspicion.

    In regard to the loss of the "word as my bound" compact, I see a new morality emerging around the consumer/service economy. Aside from energy challenges, the modern economy seems less explained by material constraints than ever. What type of social contracts are needed in this world where uncertainty reigns in consumer preference, r&d results, or ideas for new products nobody has ever demanded?

    Like you, I think the financial industry has mostly its own reclusive persona to blame for the current state of its public relations. Even if you look at the most public representative, Romney, you see a failure to enagage people about the merits of finance for the public good. But the economy of the future could belong to the society that best sustains the ("protestant") risk-ethic.


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