Assume that an asset price $S$ is given by a Brownian motion. Argue from the definition why it is not possible to predict future values of the asset based on the past values of $S$.

I am not sure exactly what this asks. I know that Brownian motion is a random process with independent increments (at least the way we defined it in our course). I am not sure what else I can add on or how I can formalise my argument more using the definition of Brownian motion.

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    $\begingroup$ Focus on the “independent increments” $\endgroup$ – dm63 Apr 14 '19 at 11:48
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    $\begingroup$ Also could help if you mention the Markov property of the brownian motion. So it's expected future values only depend on its present value and the past values do not have any bearing on what is expected in the future. But I think the general argument is just that the brownian motion isn't deterministic so future values only depend on the present value, and that future increments are entirely random (other than the drift) $\endgroup$ – Slade Apr 14 '19 at 13:58

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