The problems with derivatives stem from the fact that we price them using models that are based on assumptions and simplifications, and not everyone in the industry pays close enough attention to the details of those assumptions.
On the other hand, I do think there are mathematical problems connected to the social sciences that are just as difficult as any that arise in physics. Didier Sornette told that he was drawn to economics because the problems were so much more difficult than in physics. But these problems aren’t really connected to derivatives contracts.
Jim Simons, one of the co-founders of Renaissance Technologies, whose Medallion Fund is the most successful hedge fund ever, made very important early contributions to string theory. So perhaps Medallion has drawn on some of his early work, though Simons isn’t very forthcoming about Medallion’s strategies.
One of the ideas due to Eric Weinstein and Pia Malaney, is connected to high energy particle physics—specifically to Yang-Mills gauge theory, which is the basis for the Standard Model of Particle Physics. Weinstein and Malaney, and some others such as Lee Smolin from the Perimeter Institute, have explored how the notion of “path dependence” in Yang-Mills theory might be used to construct a better measure of how cost of living changes over time.
There are a lot of fascinating historical connections between physics and economics. For instance, the first American to win a Nobel Prize in economics, Paul Samuelson, was deeply influenced by the work of J. Willard Gibbs, a 19th century physicist who helped invent thermodynamics—and turn chemistry into a rigorous mathematical theory. Building on Gibbs, Samuelson used notions like “equilibrium” and “entropy” to explain economic phenomena. Meanwhile, the first Nobel laureate in economics, Jan Tinbergen, had a PhD in physics, and introduced the term “model” into economics, in analogy to its use in physics.
But I don’t really think it’s right to say that physics can help economics, so much as to say that there has been a rich exchange of ideas between physics and economics over the last century, and that financial professionals could benefit from learning to think about the relationship between mathematical theories and the world.
But there’s another issue that comes up in this question, concerning rigor. If anything economics is more rigorous than nuclear physics. But rigor isn’t what you need if we want to come up with useful solutions to the problems we care about. If the mathematics is right, the theories must be true. But the relationship between mathematical theories and the world is more complicated than that.
NassIm Nicholas Taleb is absolutely right about the importance of black swans—events that are completely unforeseeable, and which change everything when they occur—and of so-called “fat-tailed” probability distributions, which help us account for the likelihood of extreme events. But I think the considerations he raises, many of which should make us cautious and modest in our attempts to understand complex systems such as financial markets. I do not think they show that we should give up on mathematical modeling altogether.
No model is perfect, but surely thinking about how black swans can affect us will help us make our modeling better—not because we can ever account for every unforeseen possibility, but because the recognition that there are unforeseen possibilities can guide us in how to build extra caution into our practices. On the one hand, there’s Ed Thorp, who proved mathematically that card counting can be used to beat blackjack, and then went on to start the first modern quantitative hedge fund. He has an utterly unique way of applying mathematical reasoning to the real world.
Mathematics is an extraordinarily powerful tool. Physicists and mathematicians have made concrete contributions to our understanding of economic problems. And of course, leaving physicists aside, there are lots of economists out there who are using mathematics to understand the world’s economic problems. If tools from mathematics and mathematical modeling can’t help us understand the world’s economic problems, what else do we need? Or is the idea that economics is simply beyond the ken of human understanding?
Economics is too varied a field for the paradigm language to apply very effectively: economics has long been characterized by competing “schools”, such as New Keynesianism, Post-Keynsianism, New Classicism, Austrian economics, etc. And, especially since these tend to have political associations, it is hard to imagine a new idea coming in and leading to a complete revolution. That said, there have been a few dramatic innovations in the last 60 or 70 years that have changed wide swaths of economics.
One is game theory, which was developed in the 1940s and 1950s by mathematical physicist John von Neumann, economist Oskar Morgenstern, mathematician John Nash, and others. Game theory provided new mathematical tools for analyzing strategic scenarios, which proved extremely useful to economists. Another is the introduction of ideas and methods from the behavioral sciences, spearheaded by people such as psychologist Daniel Kahneman. This movement, known as “behavioral economics,” has successfully questioned many basic economic assumptions about rational action. I think developments such as these are the closest we will come to paradigm shifts in economics—and yes, I think they are still possible.
