Binomial Representation doubt

Joined
8/15/17
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Referring to the following article:

https://arxiv.org/pdf/1405.1948.pdf

After equation (40), it's stated that \(\phi_i\) is previsible "by definition".

But how can that be? Given any time-tick i, S(up) and S(down) are definitely not known in advance.
 
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