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Apr 17, 2022 at 10:50 comment added Maximilian Janisch This hits the quintessence but it is formulated in a misleading way: $\tilde W$ is a Brownian motion with respect to a different probability measure than $W$.
Apr 22, 2014 at 22:56 comment added fbt @AndrewDabrowski: Check out the Girsanov Theorem. It lets you transform one brownian motion into another.
Nov 5, 2013 at 14:12 comment added Andrew Dabrowski I'm puzzled by something: unless $\mu=r$ the mean of ${(μ−r)\over σ}dt+dW$ is not 0, so how can it be equivalent to anything with mean 0?
Jun 19, 2013 at 0:45 comment added Matt Wolf Did you mean to say that in a world where we can perfectly hedge the risk premium has to be equal to the risk free rate? I am asking because the asset clearly has volatility even after changing measure to a risk neutral probability measure. In fact volatility is identical before and after.
Jun 18, 2013 at 13:07 history answered SpeedBoots CC BY-SA 3.0