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

Publication Type:
Journal Article
Citation:
Japan Journal of Industrial and Applied Mathematics, 2017, 34 (3), pp. 859 - 871
Issue Date:
2017-11-01
Metrics:
Full metadata record
Files in This Item:
Filename Description Size
10.1007_s13160-017-0269-5.pdfPublished Version421.74 kB
Adobe PDF
© 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 τbassociated 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.
Please use this identifier to cite or link to this item: