在不完全观察的漂移过程中达到一个目标的最大化概率

Maximum Probability of Reaching a Goal in a Partially Observed Drift Process

对一个具有原始财产X0(<1)的投资者,当股市的涨落没有被直接观察,而仅仅是用计算的方法建立平均返回扩散模型时,他为了实现一个目标XT=1,如何达到最大的概率?在采用鞅方法的同时,以一个推广的Cameron-Martin公式就能如财富过程一样直接计算价值过程,从而采用Martin公式,可以确定动态的最优配制。

Without directly observing stock fluctuations but establishing a modal by calculation method, an investor with initial wealth XO（ 〈 1 ） wants to realize a goal XT = 1, how to reach the maximum probability？ By adopting martingale approach, a generalized Cameron - Martin formula can be used directly to calculate the value process like wealth process. So the dynamic optimal allocation can be determined by adopting Martin formula.