Tuesday, August 2, 2011

Popular Applied Math. Skills on Wall St.

Came across this at Christian Marks.

... Wall Street has begun quietly and aggressively recruiting proof theorists and recursion theorists for their expertise in applying ordinal notations and ordinal collapsing functions to high-frequency algorithmic trading

An ordinal notation system is used to name each ordinal in a certain initial subsequence of the countable ordinals; such systems have recently been applied by elite trading operations to the parameterization of families of trading strategies of breathtaking sophistication. Ordinal notation high-frequency trading algorithms, also called ordinal arbitrage systems, pit their strategies against similar algorithmic opponents on electronic exchanges for a few fleeting seconds, during which thousands of trades are executed, including exploratory trades that test the strategies of opposing human and machine traders.

The monetary advantage of the current strategy is rapidly exhausted after a lifetime of approximately four seconds–an eternity for a machine, but barely enough time for a human to begin to comprehend what happened. The algorithm then switches to another trading strategy of higher ordinal rank, and uses this for a few seconds on one or more electronic exchanges, and so on, while opponent algorithms attempt the same maneuvers, risking billions of dollars in the process. The elusive and highly coveted positions for proof theorists on Wall Street, where they are known as trans-quantitative analysts, have not been advertised, to the chagrin of executive recruiters who work on commission. Elite hedge funds and bank holding companies have been discreetly approaching mathematical logicians who have programming experience and who are familiar with arcane software such as the ordinal calculator. A few logicians were offered seven figure salaries, according to a source who was not authorized to speak on the matter.

Set Theory is Ph.D material. Game theory is postgrad as well, and is probably also a necessity to accomplish the above. Is it really necessary to learn all this to make money? Probably not. At the same time, Wall St. technology and application of advanced mathematics are growing so rapidly that it would likely become necessary to understand these concepts to go toe to toe on the institutional level.

Here's a research paper applying a Set Theory based algorithm to trade Indian stocks for a positive expectancy.

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