308 reputation
24
bio website
location
age
visits member for 3 years, 9 months
seen Oct 9 at 15:55

Sep
30
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.
Sep
24
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.
Feb
27
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.
Feb
23
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
Jan
24
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?
Jan
24
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)
Jan
24
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