The development of mathematics has influenced the development of finance theory. Commentators believe that the development of complex mathematical model is partly responsible for the deepening of the recent financial crisis. No doubt, mathematics has equally advanced the development of finance theory, and the finance discipline. In what negative and positive ways does mathematics influence the finance discipline?
Just to start the discussion on this very difficult question:
"On a visit to the London School of Economics in 2009, Queen Elizabeth asked with regal bluntness why it was that economists had not foreseen the crisis. Ten authoritative British economists then wrote to her claiming that one of the main reasons for the profession’s failure to give timely warning of the imminent crisis was the inadequate training of economists with its overriding concentration on mathematical techniques, the fact that the predominant economic theory – economics – had become a branch of applied mathematics.
The letter drew attention to the fear that «graduate programs may be turning out a generation with too many idiot savants skilled in technique but innocent of real economic issues» expressed by a commission of inquiry set up in 1988 by the American Economic Association, an institution above all suspicion. The signatories went on to add that economic history, philosophy and psychology were omitted in the education of economists and that neither the questionable belief in universal “rationality” nor the “efficient markets hypothesis” was called into question. It was also for this reason that insufficient notice had been taken of non-quantified warnings about the potential instability of the global financial system. As they wrote, «[t]here is a species of judgment, attainable through immersion in a literature or a history, that cannot be adequately expressed in formal mathematical models.» In short, mathematics fails to take context into consideration, and this involves the risk of reductionism and bogus neutrality in the economic field." (Lucarelli, S and Lunghini G., The resistible rise of mainstream economics. The dominant theory and the alternative economic theories, BUP, 2012, p. 24)
Mathematics can help build logically consistent models in finance , and Statistics help in applying probability distributions to applied finance phenomenon and empirically testing finance theories . The negative side may be that blind application of mathematical models constrain thinking sometimes rather than promoting , and more importantly there are much limitations for empirical models and their testing . Other disciplines , such as History , and Psychology are also helpful in understanding some financial phenomenon like financial markets behavior .
I very much agree with Thomas Paul. Maths bring logical consistent models in a non-logical, non-consistent world. Research needs to be done on how practicioners work with models in finance. Especially the relationship between assumptions and modelling is critical. In practice, the quality of the model is often dependent on it's ability to serve a certain interests, instead of being rigourous.
I couldn't be overbearing in answering this. However the complex financial system are gradually unavoidably depending on mathematics and stochastic. It was always there but not to the scale it is visible this time around. The point is whether that is providing any solutions? The 'behavioral finance' people will outright disagree; on the other had the derivative hedge fund and risk management people will strongly support . But I believe the true scenario is somewhere in between. First of all modern finance can't get away with 'behavioral finance' alone, at the same time many sophisticated algorithm base machine dependent pricing could not be a penance.
The debate is overwhelming influence of mathematics and algorithms. This comes from instant pricing and decision making. Ignorance of 'behavioral' issues only assert that the algorithmic solution is only a temporary one. Nonetheless 'behavioral people' alone can't provide any acceptable platform to thousands of hedge fund managers and derivatives experts making decisions of billions ,not millions,of fortunes(!!!). Their criticism can make algorithmic solutions more susceptible but at the end of the day they do not have any strong alternatives to suggests.
The trend that become visible is that 'Finance' as a discipline has already been swallowed by Physics experts, which is little worrying. Business graduates hardy believe they will be a good choice to become a real finance expert. I assume the solution is more quantization of business core modules, while keeping the behavioral modules precisely to the minimum. Again I know it is a debatable suggestions but I just assume a practical one. Not everyone will be Black and Scholes but Black and Scholes didn't ignore the investors psychological concerns. And more importantly to appreciate the potential of 'Finance' as a discipline investors can't ignore the mathematical aspects of models like Black and Scholes. So perhaps it is not Mathematicians influencing Finance irrationally; rather Finance requiring Mathematicians inevitably. Not mutually exclusive but not going hand in hand either.
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