Let's say that s is Lichello's safe (i.e. 10%) and let S be your value (i.e. S = 1 + s )
Then Lichello's actual buy order is
pc - y * (1+s) = pc - S*y
but you assert that Lichello's buy order is of the form
S * (pc-y)
I don't see how this is possible. Of course there may be something obvious which I am not seeing.
Could you provide a mathematical demonstration of how the first expression can be transformed into the second. (Of course the two S factors would be different.)