A make-your-mind-up option is an American derivative with delivery lags. We show that its put option can be decomposed as a European put and a new type of American-style derivative. The latter is an option for which the investor receives the Greek Theta of the corresponding European option as the running payoff, and decides an optimal stopping time to terminate the contract. Based on this decomposition and using free boundary techniques, we show that the associated optimal exercise boundary exists and is a strictly increasing and smooth curve, and analyze the asymptotic behavior of the value function and the optimal exercise boundary for both large maturity and small time lag.

谨慎选择是交付延迟的美国衍生产品。我们表明，它的看跌期权可以分解为欧洲看跌期权和一种新型的美式衍生工具。后者是一种期权，投资者可以从中获得相应欧洲期权的希腊θ作为运行收益，并确定终止合同的最佳停止时间。基于此分解并使用自由边界技术，我们证明存在关联的最佳运动边界，并且该曲线是严格增加且平滑的曲线，并分析了成熟度大和时滞小的值函数和最佳运动边界的渐近行为。