20,854 reputation
23170
bio website dcsc.tudelft.nl/~itkachev
location Leiden, Netherlands
age 27
visits member for 3 years, 11 months
seen 6 hours ago

I am a PhD student at TU Delft, working in applied probability and stochastic optimal control. My current focus is on approximate model-checking of stochastic systems via bisimulations (a part of computer science). I am interested in a wide field of applications, in particular in some areas of finance, such as risk theory.


6h
comment Algorithm for risky investments in banks
That's a standard example of stochastic optimal control, and can be solved using MDP techniques; there are efficient methods to solve them, if you are interested I can elaborate.
6h
comment Does this integral $\int f_{X|Y}(x|y) dy$ has any meaning in probability or statistics
I doubt that this integral has any meaning, since let's say it is representation dependent. That is, density is just one of possible representations of measures (e.g. besides the measure itself you can represent it by CDF), but this integral does not convert back to a natural (conditional) measure since you are missing the $f(y)$ term.
6h
comment The smallest filtration for which a sequence of random variables is adapted
When do we say that $X$ is adapted to filtration? Isn't it essentially as follows: $X$ is adapted to $\mathcal G$ iff $\mathcal F_n \subseteq \mathcal G_n$ for all $n$?
1d
comment Solving simple decision-making model over multiple periods
currently it seems that you have Bellman equation for the case where you can try solving the problem, and getting rewarded, as much as you want. More crucially, is the cost discounted as well? Anyways, it seems that the best solution is to maximize $p(x) V - c(x)$ as your decisions do not affect the future dynamics.
1d
comment Solving simple decision-making model over multiple periods
Can you solve problem several times, or just once?
1d
revised Solving simple decision-making model over multiple periods
edited tags
1d
comment Definition of conditional probabiliy as function dependent on $\sigma$-Algebra
@Stefan: indeed (if coincidence at all)
1d
answered Definition of conditional probabiliy as function dependent on $\sigma$-Algebra
1d
comment Probabilistic implications of the existence of non-measurable sets
related MO thread
1d
answered Can a chain with repeated nodes still be considered a Markov chain?
1d
revised Solving a PDE with Feynman-Kac Formula
added 393 characters in body
1d
comment Solving a PDE with Feynman-Kac Formula
@Carl: exactly.
1d
comment Borel measurability is a local property
You can take $x$ being rationals
2d
comment Compacticity of distribution functions
Not sure whether this can be assumed. We can approximate Dirac measures by strictly increasing CDFs in weak topology, hence the collection of latter is not compact.
Dec
14
asked Robustness of Markov Chains
Dec
14
comment Compacticity of distribution functions
Consider a set of closed and convex probability set of measures that's not really clear.
Dec
14
comment Compute almost sure limit of martingale?
If $Y_m = 1$ then the limit is $1$
Dec
14
comment Prove that risk function is analytic?
What do you mean by analytic?
Dec
14
comment Ito integral's zero mean
@BCLC: click me
Dec
14
answered Ito integral's zero mean