On distibutions of first passage times of martingales arising in some gambling problems

Publication Type:
Journal Article
Japan Journal of Industrial and Applied Mathematics, 2017, 34 (3), pp. 859 - 871
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10.1007_s13160-017-0269-5.pdfPublished Version421.74 kB
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© 2017, The JJIAM Publishing Committee and Springer Japan KK. Using a martingale technique we derive bounds and asymptotics for tail distributions of first passage times τb associated with crossing a level b for some gambling strategies. In particilar, for the case of martingale games with so-called “Oscar strategy” we show that P{τb>n}≤Cn-3/2 for any level b> 0.
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