Amarts have very good properties. This paper gave the four equivalent propositions of R-Value's amart and their proofs by utilizing the theory of stopping time.

渐近鞅型序列具有很好的性质，本文给出实值渐近鞅的四个等价命题，并应用停时理论对它们予以证明。

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Then, for a given equivalent martingale measure, the optimal stopping problem of the permanent American option is solved.

本文在一个合适的等价鞅测度下，给出了带有事件风险的永久美式期权的定价及其最优停时。

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