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 Sep30 comment Law of a geometric brownian motion first hitting time (formula dont match Monte Carlo Simulation) An interesting reference using similar arguments seems to be "How Likely is it to Hit a Barrier? Thoretical and Emperical Estimates" by Lujing Su and Marc Oliver Rieger. Sep24 comment Probability of touching An interesting reference using similar arguments seems to be "How Likely is it to Hit a Barrier? Thoretical and Emperical Estimates" by Lujing Su and Marc Oliver Rieger. Feb27 comment Threshold calculation for buying a mean-reverting asset An interesting paper could be: Yingdong Lv & Bernhard K. Meister: Application of the Kelly-Criterion to Ornstein-Uhlenbeck Processes. But they don't have the a finite time deadline. However, you could use their results to estimate the optimal trading strategy and do some Monte Carlo to incorporate the finite time horizon. However, I have to say that I didnt read the paper in detail. Feb23 comment Taylor series expansion (Volatility Trading book) explanation sought The author of the book "Volatility trading" (there will be a new edition in 2013) is quite active on nuclear phynance, there is even a long thread on the book: nuclearphynance.com/Show%20Post.aspx?PostIDKey=110391 Jan24 comment Robust-Bayesian optimization in Markowitz framework Continuing the last comment: This gives us $-|\chi||\omega|$ (because $\cos(\delta)$ is $-1$ at that angle). If we now use the notation $\chi=|\chi|$ and $\chi$ being in the interval $[0,1]$ by assumption, we arrive at equation (3). Does that explanation help? Jan24 comment Robust-Bayesian optimization in Markowitz framework From eqn (2) to (3), we want to have the worst possible r. The first term on the right side of (2) is constant in our setting given our initial $\vec{\alpha}$ and $\vec{\omega}$. Now, we want to reduce that by as much as possible. In $\chi'\omega|\alpha|$ |\alpha| is again constant, so we are looking for the smallest value of $\chi'\omega$. This can be written as $|\chi||\omega|\cos(\delta)$ with $|\chi|$ and $|\omega|$ the length of the vectors and $\delta$ the angle between them. This is minimal for $\delta=\pi$ (ie both vectors have 180 degrees between them and look in opposite directions) Jan24 comment Robust-Bayesian optimization in Markowitz framework Regarding the references, I just glimpsed over the nice working paper from Golts and Jones (2009) you cited and the pdf version of an article by Goldfarb and Iyengar (CORC Technical Report TR-2002-03 Robust portfolio selection problems). There, equations (4) and (15) seem to state the same result. Regarding the mathematical steps, I will edit my answer