第一通道思想在金融中的一些应用
Some applications of first-passage ideas to finance
摘要：
金融中的许多问题都与首次通过时间有关。在所有这些项目中，我们选择了三个，我们亲自参与了。我们的第一个例子与Kolmogorov-Smirnov相似的拟合优度测试，以这样一种方式进行修改，即尾部事件和核心事件对测试的贡献相等（在标准的Kolmogorov-Smirnov中，尾部对拟合优度的测量贡献很小）。我们表明，这个问题可以映射到移动墙内的随机行走。第二个例子是出售资产的最佳时间（建模为具有漂移的随机游走），使得出售时间尽可能接近资产达到其最大值的时间。最后一个例子涉及存在交易成本的最优交易。在这种情况下，最佳策略是等待预测值达到（正或负）阈值后再买入或卖出。这个阈值的值是通过将问题映射到两堵墙之间的随机行走问题上来找到的。
英文摘要：
Many problems in finance are related to first passage times. Among all of them, we chose three on which we contributed personally. Our first example relates Kolmogorov-Smirnov like goodness-of-fit tests, modified in such a way that tail events and core events contribute equally to the test (in the standard Kolmogorov-Smirnov, the tails contribute very little to the measure of goodness-of-fit). We show that this problem can be mapped onto that of a random walk inside moving walls. The second example is the optimal time to sell an asset (modelled as a random walk with drift) such that the sell time is as close as possible to the time at which the asset reaches its maximum value. The last example concerns optimal trading in the presence of transaction costs. In this case, the optimal strategy is to wait until the predictor reaches (plus or minus) a threshold value before buying or selling. The value of this threshold is found by mapping the problem onto that of a random walk between two walls.
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