My Math Forum Kelly Criterion

 June 14th, 2012, 06:51 PM #1 Newbie   Joined: Jun 2012 Posts: 2 Thanks: 0 Kelly Criterion I have a question about the Kelly Criterion that hopefully someone can help me answer. If you have't heard of the Kelly Criterion here is some info on it: http://en.wikipedia.org/wiki/Kelly_criterion Basically you start with a certian amount of money to invest. You also have an investment. It tells you how much of your total amount to invest to maximize gains while at the same time minimizing your chances of going broke. For example: You have 1000 dollars to invest and you can make as many investments as you want, but the only invest you can make is a 60/40 investment. In other words you will double what you invest 60 percent of the time and 40 percent of the time you will lose what you invest. The Kelly Criterion tells you that should invest 20 percent of your total 1000. So you would keep investing 20 percent of the total amount over an over. This would maximise your profits while minimizing your chances of losing the entire 1000. Thats the basic idea. I have a question with some added variables. Say that I can make 1 investment per day/min/year. Every day though I lose 100 dollars as a fee for being able to invest I don't take the investment or I lose lose on the investment. How would I incorporate this into the formula? The reason I want to know this is because it appears once a fee is involved there would by times when you would want to accept a negetive expectation investment. Here's an example of what I'm talking about: Say you have 200 dollars left, but now you are losing 100 a day on a fee. Your chances of winning is 40 percent and your chances of losing are now 60 percent. If we don't take the investment we will lose all of our money in 2 days. So in this situation it seems we would want to take the investment. So if you have 1000 dollars and you are losing 10 dollars a day at what point do you start investing on an investment you lose on 60 percent of the time and how much of your total money do you invest to minimize your chance of going broke/lose your money as slow as possible? It seems like we could modify the kelly criterion in some way to get something similar to this. If I'm thinking about this wrong or it doesn't make sense please let me know.
 June 23rd, 2012, 02:20 PM #2 Newbie   Joined: Jun 2012 Posts: 2 Thanks: 0 Re: Kelly Criterion Anyone have any thoughts?

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