Friday, 22 October 2010

Warning, Math Inside!

Next year the International Mathematical Olympiad (http://www.imo2011.nl/) will be held in the Netherlands. This calls for a celebration of math, but at present mathematical modelling seems to get the blame for all the economical problems we have. To name a few, the models from David X. Li are blamed for causing the credit crunch. The risk assessment models of banks failed; nearly tipping them over if it wasn’t for the government support they received. Also the losses incurred by the pension funds are blamed on mathematical models. In pointing the finger on who’s to blame for al this, many decision makers point to math modelling. It’s far too complicated, they say. It is however invalid to blame math for this; after all it is not the math that makes the decisions. What is to blame is the ignorance with which math models are applied. It’s like buying a state of art electronic device and getting mad at it because it doesn’t work. But if you had read the manual, things get different.

The essence of math modelling is to describe reality in mathematical terms with a specific purpose, like determining the value of an investment portfolio or assessing the risk of a project. A mathematical model always is a simplification of reality. If the model would be as complex and as detailed as reality, it would become as expensive and as difficult to use. Math allows us to focus on the essence of the question at hand and gives us the opportunity to experiment without having to perform tests in real live. No one would think of flying in a new aircraft, without first testing its ability to fly using a math model. After using the model to perform the required analysis, the results are translated back to reality. In both translations (from reality to model and back again) common sense, simplifications, assumptions and approximations are used. The model user and decision maker must be well aware of that.

A well build math model can be a very powerful instrument; you can compare it with a chainsaw. In the hands of a well trained annalist the math model will be an excellent and effective tool. In the hands of an ignorant user it can do a lot of harm, even to the user. A decision maker must know the scope, concepts and dynamics of the models used before adopting its results in decision making. This doesn’t imply that every decision maker should a well trained and skilled mathematical modeller or that the detail and complexity of the model is restricted by the decision makers’ math capabilities. An aircraft pilot for example exactly knows the scope and conditions for using the autopilot of the aircraft, this doesn’t imply that the pilot can build one himself.
Robert Merton states in his Nobel price speech in 1997:

"The mathematics of models can be applied precisely, but the models are not at all precise in their application to the complex real world. Their accuracy as useful approximations to that world varies significantly across time and place. The models should be applied in practice only tentatively, with careful assessment of their limitations in each approximation."

He is absolutely right about it, but it’s forgotten easily. Robert Merton himself failed to keep this in mind and as a result Long Term Capital Management went down in 1998.

As an operations research consultant I use math models all the time. It is tempting to keep the detail of the modelling out of the scope of the decision makers. But my experience is that developing models in close corporation with the decision maker is a far better way. When keeping the decision maker out of the loop, you need to do a lot of explaining after the model has been developed. Many times, when the results from the model are not as expected, it is the math model that gets the blame. However it is the ignorance of the decision maker that is the cause, they didn’t read the manual (or we didn’t explain the model well enough) Therefore developing the model in close corporation with the decision maker is a better way. It leads to better models because scope, assumptions and simplifications are discussed and agreed upon during the development process. This allows the decision maker to learn to use and understand the results of the model while it is being developed. No manual required! It is not only easier; it is also a better way, improving decision quality.
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