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1 vote
0 answers
95 views

Non-diagonalizable matrix in a discretized Ornstein-Uhlenbeck process

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}(\...
Oiler's user avatar
  • 11
3 votes
2 answers
920 views

Characteristic operator

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^...
Nameless's user avatar
1 vote
1 answer
22k views

Covariance and standard deviation relationship

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 ...
mtan's user avatar
  • 21
2 votes
1 answer
254 views

Brownian Bridge under observational error

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 ...
David Shor's user avatar
3 votes
3 answers
316 views

Finding a distribution family that is preserved under mixture.

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 ...
David Shor's user avatar
6 votes
8 answers
1k views

Reference for elementary and "cool" statistics or financial math

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 ...