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Probabilist by training. Currently working as a data scientist.

quasi dot surely at gmail


Aug
28
comment Brownian motion - first passage time
Passage time distributions for (arithmetic) Brownian motion are available in a lot of places, i.e. Karatzas/Shreve. Just take logs to reduce to that problem.
Aug
26
comment How to test that a distribution has infinite mean?
Perhaps you could take increasing subsets $A_n$ of your sample, test on $A_n$ whether the mean is greater than $a_n$, where $a_n \uparrow \infty$. If the likelihood of these hypotheses is "stable" as $n$ increases, maybe that would support the mean being infinite.
Aug
7
comment Risk neutral measure in exponential levy model
Dont have it handy right now, but have you looked at financial modelling w jump processes, by cont and tankov?
Aug
5
answered What is the significance of Relative Risk Aversion
Jun
18
comment Malliavin Calculus
I've struggled to find an easily readable introduction to the subject. Have you found anything that fits the bill? Especially one that comes at the problem from a probabilistic point of view, instead of analytic.
Jun
18
comment Malliavin Calculus
In my mostly uneducated view, one purpose is to get quantitative formulations of the martingale representation theorem, i.e. go beyond existence to actually constructing what the integrand should be in the representation.
May
31
answered George Soros models
May
23
comment Desired portfolio volume
The $p=2$ case is used in the context of minimizing hedging error in incomplete markets. So different concept but also used to select an optimal wealth.
May
23
comment Desired portfolio volume
@Pepijn: Usually, models for utility functions are assumed to be concave in $x$. This leads to the requirement that $p<1$. Note the $p=0$ case corresponds to $\log x$.
May
17
comment Desired portfolio volume
I would. The calculations unfortunately won't be as nice as with exponential utility, but doable.
May
17
comment Desired portfolio volume
An another approach is to use the power utility functions. This family of functions (which includes $\log x$), will have the property of constant relative risk aversion, meaning that a constant proportion of wealth will be invested.
May
17
answered Desired portfolio volume
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.