All Questions
Tagged with mathematical-finance st.statistics
6 questions
1
vote
0
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95
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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}(\...
3
votes
2
answers
920
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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^...
1
vote
1
answer
22k
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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 ...
2
votes
1
answer
254
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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 ...
3
votes
3
answers
316
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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 ...
6
votes
8
answers
1k
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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 ...