Economics and Finance

"I refuse to accept however, the stupidity of the
Stock Exchange boys, as an explanation of the
trend of stocks. Those boys are stupid alright,
but there must be an explanation of what happens,
which makes no use of this fact."
-- John von Neumann, letter to Stanislaw Ulam, 9 December 1939

I have taken an interest in the abuses of mathematics for purposes of enriching wealthy financiers. Back in the 1980s I read a one-page description of the Black-Scholes formula in The Economist, and I thought it was brilliant, but I have since grown fairly disgusted with field, for several reasons: 1) It's mostly fake spherical-cow applied mathematics, where you call it an equity price, but you're really just working the same old semimartingales, with no serious economic understanding behind it; 2) The real function of sophisticated mathematics is to surround risky investment strategies with an aura of mathematical certainty; 3) To the extent that mathematical research can improve investment outcomes, this mainly means that a public good (mathematics) is being used to enrich one (small) class at the expense of the general public. There are credible arguments that advanced financial instruments can be used to free up capital for productive uses, but these seem to have as much actual applicability as the now discredited argument that state socialism would overtake capitalism by avoiding redundant competition. Both depend on a naive notion of "efficiency". When advocated by starry-eyed adolescents this belief may be genuinely naive; when advocated by experienced moneymen and politicians it must be presumed to be deceptive. Financial mathematicians are, alas, by and large probably more naive than scheming, but they are naive by choice, which makes them more culpable than the students or the moneymen.

My first professional contact with the burgeoning scam of mathematical finance came when I moved to Berlin right after my PhD. One of the first seminar talks I heard there was about how a trader with insider knowledge could structure his trades so as to be undetectable to regulators. Pretty shocking anomie. I asked members of the large stochastic finance group how they could justify treating research on important matters of public interest in such a cavalier fashion. It's all fake, they uniformly said. We're not really doing anything that would be of use in the real world. That's just a story we tell to get our abstract mathematics research funded.

My first writing on the subject was a response*  to this article** by David Hand in the Newsletter of the London Mathematical Society, which tried to absolve the financial mathematicians of responsibility for the crash of 2007-8. I was particularly shocked by Hand's dismissal of the executives of failed banks and investment funds who relied upon the confident pronouncements of the stochastic finance guild, without recognising that it all depended Lemma 3.1.7 could only be satisfied by a market with two non-interacting investors with perfect information making frictionless transactions in a vacuum: "If I jumped into the cockpit of a Boeing 747, and crashed it because I didn’t know how to fly it, you would hardly blame Joe Sutter, the 747 chief engineer." My response, in a nutshell, was "Who did you think was going to be flying the plane?"

I later wrote at more length on the subject in the context of a review in the Notices of the AMS, of the book The Quants, by Scott Patterson. (The published version was cut down from a somewhat longer version, that you can read here.) The opening paragraph responds obliquely to the peculiar referee report that I received, from an anonymous financial services insider, who based the report not on any acquaintance with the book being reviewed, but with reviews of the book on The referee's summary was "The book is an attack on modern finance and as far as I can tell Steinsaltz is along for the ride." I was astonished, because Patterson is so obviously entranced by all the brainy Croesi that it's a challenge to pick up on hints of criticism amid the accolades. The referee (and most of the commenters, so far as I can see) are presumably plagued by guilty conscience, so that anything other than effusive praise torments their sensibilities. One sees the same psychology at work when reading the pre-Civil War debates on slavery in the U.S. (and post-Civil War debates on the Civil War). (And one of the most interesting things I've learned in recent readings about antebellum US slavery was the extent to which finance -- in particular, preserving the value of capital invested in slaves by extending the slave market -- drove the Southern demands for expansion that made war inevitable.)

Some of my comments on finance-related themes from the past few years: The mathematical finance kraken, The weird probabilistic logic of credit rating agencies (with further comments here), Default contagion, The collapse of the Euro, Charitible tax deductions, Metaphors of the stock market, and Some comments on intergenerational equity, and the distinction between rioters and tax cheats.

And here is a mock-Shakespearean sonnet, mediating between the language of money and the language of love.

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* Click on "News" and scroll down to "Mathematics or Mismanagement".

** Click on "News".