Ilya

846 reputation

215

bio	website	dcsc.tudelft.nl/~itkachev
	location	Leiden, Netherlands
	age	25
visits	member for	2 years, 4 months
	seen	Jun 6 at 17:32
stats	profile views	144

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.

	846 reputation	bio	website	dcsc.tudelft.nl/~itkachev	visits	member for	2 years, 4 months
215 badges		location	Leiden, Netherlands		seen	Jun 6 at 17:32

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Jun 12	awarded	Popular Question
Jun 4	comment	George Soros models NP, I just updated my description recently so it might have not been there before
Jun 3	comment	George Soros models Well, I am familiar with principles of the stochastic optimal control and dynamic programming. Surely, you can incorporate the reflexivity there - my question was rather on how to incorporate it in a practically meaningful way, that's why I've whether there are some financial models known that involve reflexivity as per Soros.
Jun 3	comment	Why does Black-Scholes equation hold on continuation region of American Option? For the American option, the solution is given by a Optimal Stopping/Free-boundary Problem. Here you seem to have European vanilla one
Jun 1	comment	George Soros models That's indeed interesting, a very recent paper - thanks!
Jun 1	answered	Mathematical theories of (sub)-optimal trading strategies under “idealized” assumption - price is random process known to trader
May 31	comment	Monte Carlo simulating Cox-Ingersoll-Ross process Cool! nice to know you didn't leave it at all :)
May 31	comment	Standard Assumption Terminology Just to clarify: do you mean market models, and so assumptions about the markets?
May 31	comment	George Soros models +1 `Stochastic control is one area where some reflexivity is indeed present by definition.` - can you be more specific here?
May 31	comment	Monte Carlo simulating Cox-Ingersoll-Ross process I understand your point, thx
May 30	comment	Monte Carlo simulating Cox-Ingersoll-Ross process Thanks, I'll do that! (Btw, did you leave MSE?)
May 30	comment	Dynamic hedging strategy example Did you try using general method where the portfolio has to be a martingale like the one I suggested here?
May 30	asked	Monte Carlo simulating Cox-Ingersoll-Ross process
May 30	comment	Mathematical theories of (sub)-optimal trading strategies under “idealized” assumption - price is random process known to trader What about Stochastic Dynamic Programming developed by Bertsekas et al? If you know the distribution of the stochastic process exactly, you specify admissible controls for the trader - and then you get the optimal solution. The theory is very rigorous and works for analytic spaces, so it shall be enough for your case. By the way, I would say that one needs to know joint probabilities rather than 1-time-moment distributions.
May 21	comment	Replicating strategy in the Black-Scholes model sorry, I've been away. Nice that you realize it yourself. Anyways, this is a common method of finding a replicating portfolio.
May 21	revised	Parameter estimation of Ornstein–Uhlenbeck and CIR processes edited title
May 21	comment	Parameter estimation of Ornstein–Uhlenbeck and CIR processes Well, you can find $\beta$ and $\sigma$ by using the quadratic variation of a process - no filtering is needed in such a case. W.r.t. $\alpha$ and $\theta$ you can use the UKF as Veeken suggested, or perhaps some particle filters. I am not an expert on filtering, but I'm pretty sure that both methods have their own advantages in your case.
May 21	comment	Replicating strategy in the Black-Scholes model yes, I mean that if you replication portfolio is of the form $$ \mathrm dX_t = \beta_t\mathrm dB_t + \gamma_t\mathrm dS_t $$ and it is self-financing, then $\frac{X_t}{B_t}$ has to be a martingale.
May 21	comment	Distribution of profit/loss for retail traders in FX +1, but unlikely such statistics exist due to the reasons mentioned by @user2183336. What I've seen is mostly purely empirical estimates in introductions of books on technical analysis, together with reasons why so many people fail. In such a case, perhaps Taleb's book is worth reading.
May 21	awarded	Organizer