漂移布朗运动的最优加倍点

Optimal Doubling Points for Brownian Motion with Drift

在利用布朗运动进行的赌博中 ,若允许在某时刻对赌本进行加倍 ,并且在每轮赌局中允许加倍的最多次数限定为 n ,Ross SM( 1 988)与罗乔林考虑了当 n=∞时最优加倍点的选取问题。在对带漂移的布朗运动考虑了类似的问题 ,对任意的 1 n ∞ ,都具体给出了各次最优加倍点 ,推广了Ross与罗的结果 。

Suppose that doubling the stake is permitted in the gamble of Brownian motion and the total numbers of doubling times in one round is limited by n, 1 [less-than or equal to] n [less-than or equal to] infinity , Ross S M(1983) and Luo Qiaolin (1992) discussed the problem of optimal doubling points as n = infinity . In this paper, a similar problem for the Brownian motion with drift is investigated, and, for any natural number n, those n doubling points are given, which extend the results in Ross and Luo, simultaneously, properties of these doubling points are considered.