American Derivative Securities. Presenter:Ting-Hsuan Long. 8.1 Introduction. 8.2 Stopping time. Discrete time Continuous time should be in F(t). Definition8.2.1. A stopping time is a r.v taking values in [0,∞] and satisfying (8.2.1). Remark8.2.2.
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should be in F(t)
depending on whether .
In either case,
In this interval, . is in the set
We have shown that A
Let and X has a continuous path, we see that . It follows that .
We have shown that
Under these two step,
Because there are only countably many rational numbers q in [0,t], they can be arranged in a sequence, and the union
is really a union of a sequence of sets in F(t).
We conclude that A