Continuing my rant on incompetency, the problem of poor general mathematical culture seems to be pervasive among financial mathematics (financial engineering, mathematical finance, computational finance, whatever catchy name universities come up with) students. I have a few favorite embarassments that I witnessed personally. The first happened in the middle of lecture on risk management when a student (who during introductory lecture boasted her advanced degree in statistics) asked why there was a division by n-1 (and not just n) in the formula for sample standard deviation. The lecturer probably thought it was hopeless to say words like “unbiased” and just resorted to “degrees of freedom” handwaving. I found the whole situation extremely ironical given the environment of graduate math program.
My second example shows the level of knowledge that students choose (not) to maintain after a class is over. A student is asked what Girsanov theory is about. This particular student has just finished rather technical class on fixed income derivatives and “sat through” two quarters of stochastic calculus a year ago. The answer he manages to come up with is literally “Girsanov theory helps us to switch to risk-neutral world where all math works out easily”. That is it. The word “measure” is not even mentioned.
Finally, the last case comes not from university but from, disturbingly, real life. A person calling herself quantitative analyst explains PCA to other “quants”. At some point she casually explains that eigenvalues are equal to lengths of corresponding eigenvectors. All the “quants” seemed quite comfortable with the explanation.
All those (and many other) observations draw some joyless conclusions, notably that financial mathematics jobs attract herds of people with abysmal mathematical capabilities. It also may just be the consequence of general decline in mathematical education (brilliantly illustrated in this paper by Vladimir Arnold). What is worse, majority of those people manage to get the jobs and that is not surprising at all given the fact that majority of hiring managers in not a top tier firms are MBA types with vague understanding of math. It would be hard to imagine those “mathematicians” thriving in a demanding environment which would put their skills to real test.
More examples for my collection are welcome.
