But financial mathematics has been underfunded, given its economic importance, and both private and public sectors must commission more research in the field. For instance, we need to know more about the way human psychology affects market models – and about the scenarios in which models break down.
Saturday, 21 March 2009
I was very pleased to see the FT's leader today, "Maths and markets". It robustly defends mathematicians from responsibility for the financial crisis (an odd assertion of Lord Turner's).
Not only that, but it also points to an interesting behavioural question:
The need to blend psychology and mathematics is not often recognised, and it's good to see the FT coming around to it. I absolutely agree with this, needless to say - both Intellectual Business and Inon continue to work on mathematical modelling of human decision-making and working out its consequences at the market and macroeconomic level.
That sentence does contain a subtle kicker at the end: "the scenarios in which models break down". Assuming they are not referring to this story, this raises the intriguing idea of mathematics which can describe its own failures.
Now on a philosophical level, we have been there before. But in practice this is likely to express itself in simpler ways. We can always build and use more than one model at once. A detailed model, perhaps, of psychology and decision-making under various conditions, linearised within the bounds of typical rates of change, and valid when there are sufficient decision-makers in a population to make statistically significant predictions. A different model to be used for smaller groups, perhaps with less predictive power or requiring more input variables. And another one which makes far less specific predictions but may still be able to offer general behavioural laws which apply when the preconditions of the detailed model are violated.
Of course in physics we have several models just like that - quantum mechanics (and even within that, several different simplifications), classical Newtonian or electromagnetic models, and the special and general relativistic versions. Each one has its domain of applicability and breaks down when pushed to certain extremes. The breakdown, in fact, simply shows where we don't yet have the facts to extend the theory - which is what drives many of the major experiments in physics. The LHC and the space telescopes of the last twenty years, for example, are mainly there to get data to fill in the known gaps of our models.
No doubt we will be able to devise similar experiments in economics. It's unlikely we can also get access to the same kind of budgets - at least from the public sector. But there is so much money at stake, not just in the financial economy but the real one, that a cunning behavioural economist will easily be able to persuade private firms that it's worthwhile to invest in this research.