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Dec
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Dec
10
comment Examples of non-increasing variance of a time homogeneous Markovian process
Variance is strictly increasing if the value at time zero is deterministic. It's not true if the initial value is random, i.e. the steady state. Exponential decay of the initial value /steady state contributes decreasing variance over time to balance things out.
Dec
9
comment Examples of non-increasing variance of a time homogeneous Markovian process
en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process; start it from its steady state distribution. note this has mean-reverting behavior, similar to your example. oops, doesn't start at 0 though
Dec
9
comment Examples of non-increasing variance of a time homogeneous Markovian process
gotcha, get it now
Dec
9
comment Examples of non-increasing variance of a time homogeneous Markovian process
"variance periodically oscillates over time"...that doesn't sound time homogeneous to me
Dec
9
awarded  Critic
Nov
30
answered Problems to understand a stochastic DGL equality
Nov
15
comment Library for interactive financial charts
I use Spotfire for some exploratory analysis (it's quite intuitive, but can't do super sophisticated stuff) and also publishing interactive dashboards. Heard similar good things about Tableau. I think there are free/trial versions of these things, but not completely sure. There is an R plugin for Spotfire, but I haven't used it personally.
Nov
14
comment Portfolio risk decreased by increasing share of riskiest asset?
That riskiest asset is negatively correlated with all the other assets in your portfolio?
Nov
10
comment What is the stochastic differential of a general semimartingale?
You'll only get a PDE if your underlying process $H$ is diffusion. If you add a Poisson or Levy process, you will get a PIDE, which has an integral term in it: this results from the non-localized nature of the jumps that $H$ can take. The Levy-Khinchin formula calculates the characteristic function in terms of $H$'s characteristics, so that might be what you're looking for. But, if $H$ is a general semi-martingale like you described, I believe the characteristic function will satisfy a stochastic PDE, which is studied, but not that widely.
Sep
16
awarded  Custodian
Sep
16
reviewed Approve IB TWS & API, without IB account?
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.