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You said that the PX_BID and PX_ASK values are dependent upon when you pulled the data. But if I pull historical data (e.g. for the last month) only the value of today would be changing but not the past ones... So there should be a point of time when the final PX_BID and PX_ASK values for a day are calculated. Or am I wrong?


For simplicity, we assume the necessary positivity, and then we can ignore the absolute signs. Note that \begin{align*} \big(C_1 - a e^{-bt} \big) d\omega = \big(C_1 - a e^{-bt} \big) f(t) dt + cbe^{-bt} \omega dt. \end{align*} That is, \begin{align*} \big(C_1 - a e^{-bt} \big)\,d\omega - cbe^{-bt} \omega \, dt= \big(C_1 - a e^{-bt} \big) f(t)dt. ...

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