有向可预报时的定时：斜布朗运动的最优停止
Timing in the Presence of Directional Predictability: Optimal Stopping of Skew Brownian Motion
摘要：
我们调查一类最优停止问题中产生的，例如，研究考虑的时间不可逆的投资时，基本遵循斜布朗运动。我们的研究结果表明，当地的方向预测模型的存在下的斜点有一个不平凡的，有点令人惊讶的影响决策者的时间激励。我们证明了等待总是最优的斜点为一大类的运动回报。这一发现的一个有趣的结果，与依赖于普通布朗运动的研究形成鲜明对比，即即使收益是线性的，问题的练习区域也可以变得不连通。我们还建立了较高的偏度增加了等待的动机，并推迟了投资机会的最佳时机。我们的一般结果明确说明了分段线性回报。
英文摘要：
We investigate a class of optimal stopping problems arising in, for example, studies considering the timing of an irreversible investment when the underlying follows a skew Brownian motion. Our results indicate that the local directional predictability modeled by the presence of a skew point for the underlying has a nontrivial and somewhat surprising impact on the timing incentives of the decision maker. We prove that waiting is always optimal at the skew point for a large class of exercise payoffs. An interesting consequence of this finding, which is in sharp contrast with studies relying on ordinary Brownian motion, is that the exercise region for the problem can become unconnected even when the payoff is linear. We also establish that higher skewness increases the incentives to wait and postpones the optimal timing of an investment opportunity. Our general results are explicitly illustrated for a piecewise linear payoff.
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