This is an elementary mathematical finance article. This means if you know some math (linear algebra, differential calculus) you can find a quick solution to a simple finance question. The topic was inspired by a recent article in The American Mathematical Monthly (Volume 117, Number 1 January 2010, pp. 3-26): “Find Good Bets in the Lottery, and Why You Shouldn’t Take Them” by Aaron Abrams and Skip Garibaldi which said optimal asset allocation is now an undergraduate exercise. That may well be, but there are a lot of people with very deep mathematical backgrounds that have yet to have seen this. We will fill in the details here. The style is terse, but the content should be about what you would expect from one day of lecture in a mathematical finance course.
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New paper: A Discrete Model Gauging Market Efficiency PDF
We highly recommend reading the PDF version, but please find below a HTML translation of the paper.
We follow up on some interesting work from the literature and explore some conditions that allow large predatory traders to dominate markets.
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A bit of a tempest in finance news involving accusations of sensitive code stolen from a major trading desk. For emerging details see:
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What does the market think about IBM’s proposed acquisition of Sun? Read more…
There is plenty of blame to go around from the current global financial crisis. But, I would like to point out that it is not “all the quants’ fault.” We are all now, unfortunately, sitting in the middle of a high quality (and extremely expensive) lesson in financial mathematics. I would hate for some of the truly important points to be lost to paying too much attention to some of the shiny details.
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The current state of the global financial markets has gotten more people than usual worrying about the technical aspects of finance. One method for reasoning about investment returns and risk is a tool called the Sharpe Ratio. It is well worth reviewing this measure and seeing how, if used properly, it doesn’t favor any of the mistakes that underly our current financial crisis. Read more…
Betting Best of Series is a new expository paper describing the mathematics involved in betting on something like the United States’ Major League Baseball World Series. It isn’t so much about baseball as about demonstrating some of the really great ideas from mathematical finance in a simplified setting. This sort analysis is the “secret sauce” in a lot of financial models and I trying to share the thrilling feeling of working with these techniques in an elementary essay (with diagrams). Read more…
author: John Mount, 5-13-2008
Anand Rajaraman recently wrote a very thought-provoking entry on his Datawocky blog. He asks “Is Search Advertising a Giffen Good?” As he explains a Giffen Good is a sort of economic doomsday machine that some segment of consumers are forced to buy more of an inferior good as the price of the inferior good goes up. His article is well written are really invites one to think about the issue. Anand’s question made me thing about a number of issues (which I will outline here) and I will leave off with a question of my own.
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author: John Mount
I have finally written up and released a paper in PDF: Automatic Generation and Testing of Trades describing a lot of the statistics and optimization methods used when I was technical trading on a Banc of America Securities proprietary program trading desk. It was a very exciting time.
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