All Questions

I am attempting to implement a pairs trading algorithm for two securities by approximating a discretized version of the Ornstein-Uhlenbeck process: \begin{equation*} d\mathbf{S}_t = \mathbf{\kappa}(\...

Let $X_t\in\mathbb{R}$ be an Ito diffusion process given by $$ dX_t=a(b-X_t)dt+\sigma dW_t$$, then the characteristic operator of $X_t$ is given by $$L=a(b-x)\frac{\partial}{\partial x}+\frac{\sigma^...

I would like to know if an increase in the covariance between two variables would imply that the standard deviation for one of the variables has increased? This is assuming that the standard ...

Suppose that $Z_t$ follows a simple discrete random walk $Z_t=Z_{t-1}+e_t$ , where $e_t$ are a bunch of uncorrelated normal variables with arbitrary variance sigma^2, and that there are observations ...

Consider the following $f_{t+1}(z)=p_{12} f_{t}(z/A)+ p_{21} f_{t}(z/B)+p_{22} f_{t}(z/(A+B))$, where $A$, $B$, and the $p$'s are constants and $f_t$ is a probability distribution. Are there any nice ...

I signed up for a Math Mentorship Program (for high school students) this term, but one of the students assigned to me is more interested in Statistics and Finance - something that would help him to ...