I’ve posted RWT-008, which goes over some basic game theory as it applies to a common trading decision: taking profits vs. letting the trade ride. In a canned example, I show how you can mathematically decide which option is best, and also give a way to model the imperfection of the common trader when it comes to maximizing profits. A key point is how the decision changes when you get to make a choice lots of times versus just once, and how traders irrationally seem to act as if every trade is their last!
It can be viewed here: RWT-008, or of course it is listed as #8 on the articles page.
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on Thursday, January 28th, 2010 at 4:48 pm and is filed under Mathematics, Trading.
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Interesting… but how do you determine that there is a 65% chance that the trade will go another 2 points? If I had that kind of information, I’d code up the strategy and have money rolling in like crazy. I know that’s not really the point of the article, but… applying this to trading does require being able to measure such a thing, at least if we’re going to apply it quantitatively.
Actually outside of canned games like chess, a lot of probabilities used in game theory are of the ‘belief’ sort rather than the frequentist kind. Not as directly translatable to code, I’m afraid. In the examples in the article, the trader does not act in a way to maximize his gain, based on what he believes will happen in the market. Whether that belief is based on a kind of expert opinion or a frequency count doesn’t matter.
For frequentists, “how you determine” is really no mystery, though you’ve no doubt noticed it’s really hard to find even the example 65% edge. You do it based on a stable historical frequency. The article didn’t specify, but in that example it could either be a frequency based on all trades from entry, or a conditional probability of times the trade reaches 4 points once it’s reached two and whatever other context there is.
Most people ignore (or, more likely, don’t realize) that you need a stable probability mass for your frequency counts or you are just fooling yourself. The curse of the backtester: “the damn market changed on me again.”