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tbatson
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Optimal Betting Strategies

January 27th, 2005, 10:44 pm

There has been a large quantity of literature produced over the last few decades regarding optimal betting strategies based on Kelly betting and Optimal f. The purpose of my question is not to “re-hash” these same old formulas again. I am assuming these strategies are based on zero correlation between individual trades, bet results, or whatever “game” results you are “playing”.Are there any optimal betting formulas that have been developed, to account for positive or negative serial correlation between individual trades or bet results?
 
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tbatson
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Optimal Betting Strategies

January 28th, 2005, 5:18 pm

Bump
 
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exotiq
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Optimal Betting Strategies

January 28th, 2005, 6:05 pm

Don't know about closed form, but you can (almost) always use Monte Carlo.
 
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quantie
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Optimal Betting Strategies

January 29th, 2005, 1:56 am

Well in the presence of serial correlation you should bet the maximum possible amount. But the serial correlation is known ex-post so I don't see how this information could be used?
 
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tbatson
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Optimal Betting Strategies

January 31st, 2005, 5:48 am

quantie:In the presence of "perfect" positive (+1) or negative (-1) serial correlation, you would know exactly what the next result would be, and your optimum bet would be to "bet it all". You are correct. However, what I am referring to, is when serial correlation between bets or trades is between 0 and +1, or 0 and -1. When serial correlation is zero, the optimum betting strategies are the Kelley or Optimal f formulas. Intuitively, as serial correlation approaches +1 or -1, the optimal betting percentage should increase above the Kelley percentage. But the big question is, how much more? For example, if the Kelley bet is 5% of capital, and serial correlation between your trades or bets is +.70, what is your optimum betting percentage? Intuitively, my guess is something greater than 5%, but less than 100%(since the serial correlation is not "perfect"(+1,-1),there is "risk of ruin" by betting 100%). However, that is not a very precise guess. What I would like to find is an optimal betting formula that takes into account not only the probability of winning and losing, and the payoff structure, but also the "amount" of serial correlation between trades(bets). I leave this problem to all the brilliant minds on this website.
 
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jkalman
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Optimal Betting Strategies

January 31st, 2005, 10:40 am

QuoteOriginally posted by: tbatsonquantie:In the presence of "perfect" positive (+1) or negative (-1) serial correlation, you would know exactly what the next result would be, and your optimum bet would be to "bet it all". I don't understand what you mean by "bet it all" : if there is perfect correlation it's the just the same kind of asset, that is to say you don't diversify your risk and then you shouldn't "bet it all" but rather "divide it all": if 5% was the optimal fraction bet for one asset, you should only bet half of 5% in each asset (so 2.5%) if they were perfectly correlated assets, if you don't do so your risk of ruin would increase perhaps to certainty since you would globally bet more than the optimal fraction.So instead of "as serial correlation approaches +1 or -1, the optimal betting percentage should increase above the Kelly percentage"I would rather say"as serial correlation approaches +1, the optimal betting percentage should DECREASE BELOW the Kelly percentage"As for the -1 what interest is there to invest in a position that just aims to nullify the other ? (Consider I'm a novice and so it's a genuine question ).
Last edited by jkalman on January 30th, 2005, 11:00 pm, edited 1 time in total.
 
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gjlipman
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Optimal Betting Strategies

January 31st, 2005, 3:08 pm

I remember doing some work on this years ago - and using a paper by Maslov and Zhang (http://xxx.lanl.gov/abs/cond-mat/9801240) - this should point you in the right direction. If I remember rightly, the paper had a few mistakes, but should point you in the right direction.
Last edited by gjlipman on January 30th, 2005, 11:00 pm, edited 1 time in total.
 
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tbatson
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Optimal Betting Strategies

January 31st, 2005, 4:41 pm

jkalman:I think you are misunderstanding what I am looking for. Your analysis is based on the correlation between assets in a portfolio. What I am referring to is when there is serial correlation in the actual trades in a sequence of trades. For example, if there is positive serial correlation in my trades, and I have just made a profit on my last trade, it is more likely that my next trade will also be profitable. Based on this scenario, I should bet more than the optimal Kelley percentage.gjlipman:I will take a look at the link. Thank you.
 
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jkalman
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Optimal Betting Strategies

January 31st, 2005, 5:34 pm

QuoteOriginally posted by: tbatsonjkalman:I think you are misunderstanding what I am looking for. Your analysis is based on the correlation between assets in a portfolio. What I am referring to is when there is serial correlation in the actual trades in a sequence of trades. For example, if there is positive serial correlation in my trades, and I have just made a profit on my last trade, it is more likely that my next trade will also be profitable. Based on this scenario, I should bet more than the optimal Kelley percentage.Oops poor of me I read too fast but also because in the case of trades I wouldn't imagine real special problem it would create : if there is a positive correlation of trades then you can have the probability edge - with Bayes theorem and conditional probability - and so the formulation is the same as the classical one no ? or did I misunderstand something else ?
Last edited by jkalman on January 30th, 2005, 11:00 pm, edited 1 time in total.