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Probabilist by training. Currently working as a data scientist.

quasi dot surely at gmail


May
17
comment Desired portfolio volume
Have you tried with exponential utility $U(x) = -e^{-\lambda x}$ and power utility $\frac{1}{p}x^p$?
May
16
comment Exact value of mean reversion rate knowing terminal value of the process
That's a linear ODE with a closed form solution. Have you tried using that? Solve it with separation of variables.
May
16
revised Covariance of brownian motion and its time average
added 7 characters in body
May
16
answered Covariance of brownian motion and its time average
May
16
comment Covariance of brownian motion and its time average
It looks like you're assuming that if you have $X$ and $Y$ which are equal in distribution, then for any $Z$, $\text{cov}(X,Z) = \text{cov}(Y,Z)$. This isn't true in general.
May
15
comment How to prove that markets are incomplete under the Stochastic Volatility model?
Can you show that there are multiple different equivalent martingale measures? Completeness is equivalent to the existence of a unique martingale measure. This is called 2nd Fundamental Theorem of Asset Pricing sometimes.
May
7
comment Rate Distortion Minimization in a Python Clustering Algorithm
I guess I meant that now they're algebraically dependent.
May
7
comment Rate Distortion Minimization in a Python Clustering Algorithm
Right sorry, what you said is right. But your "observations" aren't independent now. Not sure how that will affect things.
May
7
comment Rate Distortion Minimization in a Python Clustering Algorithm
The naive application of the paper you cited seems to be: calculate $\Sigma$ as you did, then use the distortion measure to cluster the $d$-dimensional returns as a function of time.
May
7
comment Rate Distortion Minimization in a Python Clustering Algorithm
So I'm a little confused. You're using $\Sigma$ as your underlying data, with each row a data point. So you have $d$ points in $\mathbb{R}^d$. But in your dispersion calculation, you're not using the covariance matrix of $\Sigma$, you're using $\Sigma$ itself. This seems to not be the algorithm.
May
7
comment Rate Distortion Minimization in a Python Clustering Algorithm
any chance you could post your data?
Apr
12
comment Ito's Lemma - Integrand depends on upper limit of integration
This isn't right. The $e^{t/2}$ term can't be treated as a constant, and there shouldn't be an $s$ and a $t$ in your final answer.
Apr
12
comment Ito's Lemma - Integrand depends on upper limit of integration
Factor out the $e^{t/2}$ part and then use the product rule. This question should be useful: quant.stackexchange.com/questions/4733/…
Apr
9
comment Non-arbitrage theory and existence of a risk premium
For your second question, do you need to assume that $\sigma_t \geq 0$?
Apr
9
comment Non-arbitrage theory and existence of a risk premium
For the first question, you should be able to use the trading strategy where at time $t$ you hold $1_B(t) \mu_t$ units of stock. This will generate an arbitrage.
Apr
9
comment Non-arbitrage theory and existence of a risk premium
In your second question, should it be $1_{t \in O}$?
Apr
3
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Apr
2
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Apr
2
comment Does the geometric Ornstein-Uhlenbeck process have stationary variance?
If it's stationary, wouldn't it be impossible for its long run variance to depend on an initial condition? Also, maybe I'm missing something, but when SKRX gives an explicit representation of the process, doesn't that directly mean your derivation is off?
Apr
1
comment Does the geometric Ornstein-Uhlenbeck process have stationary variance?
Are you sure your modified process has an equilibrium distribution? If $\sigma$ is much larger than $\theta$, intuitively you might think that it doesn't (Imagine when $S_t$ is large, the effective volatility is significantly larger than the mean-reversion). This intuition is actually reinforced by looking at the variance formula for $S_t$.