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What is the Stochastic Differential Equation for a "Brownian Motion Characterised by Sharpe Ratio"?

I saw it in a paper ("Lessons from the Mortician: volatility modulation") and the authors do not define such equation.

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  • $\begingroup$ I did not read the paper, but are you familiar with how one derives the risk neutral dynamics under the Black-Scholes model? $\endgroup$ – Andrew May 17 '18 at 20:34
  • $\begingroup$ Access to the paper seems to require a subscription... $\endgroup$ – Alex C May 17 '18 at 20:36
  • $\begingroup$ @Andrew Yes, I am! But the authors use this process to define the year to date return performed by a trader, so I think the process should have no drift, but if a Sharpe Ratio is used to parametrize it, the only way I see is to have a process with drift under measure 1 and then apply Girsanov in order to have a Brownian motion under measure 2. I really would like to see the Stochastic differential equation in order to know exactly what the author means. If you manage to get the details, I would appreciate. I tried to post a picture of the paper but it is forbiden here. Get free one week access $\endgroup$ – AnUser May 19 '18 at 23:26

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