Math Models: From financial meltdown to global warming

Computer modeling allows experts to extrapolate the implications of complex sets of assumptions and data in a timely fashion. In a few decades they have become a fundamental tool of the analyst. The computer models amplify analytical efforts in a manner analogous to the way mechanical engines amplify muscle power. Indeed we would no more be able to check the computer analysis without computers than we would be able to replace the machines in a coal mine with manual labor.

News reports suggest that an important factor in the financial meltdown at the end of the last decade was the use of mathematical models for risk management by the financial industry and its regulators. While I worked on mathematical models in another context, I don't know enough about those used in finance to comment intelligently. Still, the models that were in use must have failed to provide their users with adequate warning of the risks they were running. I would bet that the chief executives and boards of directors of the major firms involved neither had the expertise to understand the details of the models being used nor that they had taken the time to make a detailed investigation of those models on which they were betting their firms. A lot of those firms lost those bets.

Climate change is a sufficiently complex subject that powerful models must be applied to its analysis. A lot of very good scientists and modelers are doing so. Again, I am not expert in these models, but it is clear that there exist several different very strong models, indicating both the fact that there is not now an agreement on the perfect form for such a model and that the models are sufficiently robust to agree generally in their predictions. I am sure than none of the heads of government or major legislative bodies are experts in climate change nor these models. I suggest that there is a possibility that the existing models might fail to predict radical, non-linear climatic effects of factors that are not fully included in the theory or parameterization of the existing climate models.

While the bigwigs of the financial firms that got into such troubles made a lot of money in salaries and bonuses during the period in which they failed to take into account the risks that their models were wrong, the rest of us are paying for their failure in risk management.

The politicians who deny the risks that the current climate models are fatally flawed may reap short term political benefits. Let us hope that our children and their children do not pay for the failure to act now to reduce the threat of climate change. Prudence suggests that we not bet the future of the planet and the human race that the models -- which already predict major climate changes -- are not too conservative in their predictions.