Gambler’s Ruin Problem with Relative Wealth Perception
نویسندگان
چکیده
We consider a modified version of Gambler’s Ruin Problem in which the gambler decides to quit based on the relative change of his or her wealth. For this purpose we consider two possible changes of wealth, namely the upward rally and the downward fall. We define upward rally as the difference of the current wealth and its historical minimum, while the downward fall is the difference of the historical maximum of the gambler’s wealth and its current value. The gambler stops playing once either the upward rally or the downward fall reach some pre-specified levels for the first time. This paper determines probabilities of stopping on the upward rally in contrast to stopping on the downward fall both in the discrete and in the continuous time models.
منابع مشابه
Change-point detection of two-sided alternatives in the Brownian motion model and its connection to the gambler’s ruin problem with relative wealth perception
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