Martingales and Betting Strategies - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T13:38:07Z http://mathoverflow.net/feeds/question/8509 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/8509/martingales-and-betting-strategies Martingales and Betting Strategies Chris Conidis 2009-12-11T01:14:41Z 2010-09-29T18:49:08Z <p>Does anyone know of a good introduction to the theory of martingales and betting strategies from the point of view of statistics and/or probability theory? I'm looking for something basic, with lots of examples. Thanks.</p> http://mathoverflow.net/questions/8509/martingales-and-betting-strategies/8510#8510 Answer by Steve Huntsman for Martingales and Betting Strategies Steve Huntsman 2009-12-11T01:20:48Z 2009-12-11T01:20:48Z <p>I don't know about statistics <em>per se</em> but the best introduction to martingales <em>period</em> is Williams' <em>Probability with Martingales</em>:</p> <p><a href="http://www.amazon.com/Probability-Martingales-Cambridge-Mathematical-Textbooks/dp/0521406056" rel="nofollow">http://www.amazon.com/Probability-Martingales-Cambridge-Mathematical-Textbooks/dp/0521406056</a></p> http://mathoverflow.net/questions/8509/martingales-and-betting-strategies/8520#8520 Answer by Alekk for Martingales and Betting Strategies Alekk 2009-12-11T02:07:46Z 2009-12-11T02:07:46Z <p>no doubt that <em>Probability with Martingales</em> is excellent, but I am not sure that this is a very satisfying book for someone interested in "the point of view of statistics". </p> http://mathoverflow.net/questions/8509/martingales-and-betting-strategies/8530#8530 Answer by jrshipley for Martingales and Betting Strategies jrshipley 2009-12-11T04:52:26Z 2009-12-11T04:52:26Z <p>I haven't read it, but I saw Glenn Shafer give a talk on his and Vladimir Vovk's game theoretical approach to probability. It could be an interesting/more intuitive approach than the usual measure theoretic approaches. They discuss martingales in several chapters of their book and I'm certain there's lots of applications/examples especially from finance. Might be worth a look: <a href="http://www.probabilityandfinance.com/chapters/toc.html" rel="nofollow">http://www.probabilityandfinance.com/chapters/toc.html</a></p> http://mathoverflow.net/questions/8509/martingales-and-betting-strategies/10772#10772 Answer by Yuri Bakhtin for Martingales and Betting Strategies Yuri Bakhtin 2010-01-05T02:57:30Z 2010-01-05T02:57:30Z <p>Shiryaev's "Probability" is an excellent source.</p> http://mathoverflow.net/questions/8509/martingales-and-betting-strategies/40504#40504 Answer by PeterR for Martingales and Betting Strategies PeterR 2010-09-29T17:47:26Z 2010-09-29T17:47:26Z <p>Have a look at "The Doctrine of Chances: Probabilistic Aspects of Gambling" by Stewart Ethier <a href="http://www.springer.com/mathematics/probability/book/978-3-540-78782-2" rel="nofollow">http://www.springer.com/mathematics/probability/book/978-3-540-78782-2</a></p> <p>Lots of examples related to just about every casino game you've ever heard of, and a few you have not.</p>