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Probably I am just confused, but why for the exact solution of the geometric brownian motion [itex]dX_t = \mu X_t dt+\sigma X_t dW_t[/itex] we have to apply Ito's lemma and manipulate the expression obtained with [itex]dlogX_t[/itex]? Couldn't we directly use the espression [itex]dX_t / X_t = dlogX_t[/itex] in the equation [itex]dX_t / X_t = \mu dt+\sigma dW_t[/itex]?

Thank you for your help!

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# Exact Solution of Geometric Brownian Motion

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