1,029 reputation
321
bio website dcsc.tudelft.nl/~itkachev
location Leiden, Netherlands
age 26
visits member for 3 years, 1 month
seen 19 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.


Apr
15
awarded  Tumbleweed
Apr
14
comment How can the Wiener process be nowhere differentiable but still continuous?
I would be careful with such explanation, though. For example, a straight line is extremely self-similar on various scales, however it is perfectly smooth. Also, one can say that smoothness is exactly local similarity to straight lines, isn't it?
Apr
14
comment How can the Wiener process be nowhere differentiable but still continuous?
@Probilitator The gif actually looks like some old-school flight simulator in the mountain area :)
Apr
11
comment Convolution copula?
There is no need or requirement for the two copulas above to be the same. Do you mean here that $$ \mathbb{P}(X\leq x,y_{1}\leq Y\leq y_{2})=C_1(F_{X}(x),F_{Y}(y_{2}))-C_2(F_{X}(x),F_{Y}(y_{1})) $$ with $C_1\neq C_2$ in general?
Apr
10
comment How can the Wiener process be nowhere differentiable but still continuous?
@Probilitator: thanks. 3d - is some quant joke I fail to understand?
Apr
10
answered How can the Wiener process be nowhere differentiable but still continuous?
Apr
9
comment unique equivalent martingale measure in incomplete markets
Sure :) also, what does these square mean? That you take an expectation/integral of squared R-N derivative?
Apr
8
awarded  Tag Editor
Apr
8
revised market-making wiki excerpt
added 250 characters in body
Apr
8
wiki created market-making excerpt
Apr
8
suggested suggested edit on market-making tag wiki excerpt
Apr
8
accepted Particular kind of market game
Apr
8
asked EMM in incomplete markets
Apr
8
comment unique equivalent martingale measure in incomplete markets
Are you missing come expectations in the right-hand side?
Apr
8
comment How to choose a risk-neutral measure when the market is incomplete?
What is the reason to pick up $\Bbb Q$ to be closest to $\Bbb P$ w.r.t. some metric?
Apr
7
accepted Simple pricing example confusion
Apr
7
comment Simple pricing example confusion
I think I see your point: when we are making an equivalent change of measure, we have to restrict ourselves to finite intervals of time, otherwise changing the drift changes the null events. Thanks
Apr
7
asked Simple pricing example confusion
Apr
4
comment PDE pricing of barrier options in BS
Regarding PDE approach, I'd say Wilmott follows it everywhere in his books. Actually that's the same as martingale approach + Markovian structure, but without mentioning the latter two things too often (as Shreve does, in contrast) and using instead $\Delta$-hedging-like arguments, which of course leads to the same PDE as the martingale approach does. So I'd be interested in a book with a similar approach, but slightly more formal on the PDE side (not necessarily on a stochastic side). Maybe there are some known textbooks of that kind, if not - nevermind.
Apr
4
comment PDE pricing of barrier options in BS
Thanks for your answer. I actually didn't mean solution of PDEs, especially an analytic one, just a PDE formulation. At least one advantage it gives is useful formulas for Greeks. My point is that the PDE for barriers in BS is "derived" using arguments like "value of option satisfies BS before hitting the barrier", so obviously we need to solve BS equation with an additional boundary condition on the barrier. As usual, it is this obvious step that can make the whole result being incorrect - so I just wondered whether there is a detailed explanation of this.