1,029 reputation
321
bio website dcsc.tudelft.nl/~itkachev
location Leiden, Netherlands
age 26
visits member for 3 years, 2 months
seen yesterday

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.


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
May
21
comment How to simulate a Geometric Binomial Process with state/tie dependent increments?
I can write a sketch of a MATLAB code, would it help you?
May
21
comment Exact value of mean reversion rate knowing terminal value of the process
@quasi: perhaps, you can put this comment as an answer (I would upvote)
May
21
answered What's the first time-integral of price called?
May
21
comment What is a martingale?
Which definition of a random walk are you using here?
May
21
comment Replicating strategy in the Black-Scholes model
In this special case, can't you just use the fact that $\xi = \eta +K$ where $\eta = \max(0,S_T - K)$ is a claim for European call? Also, computing the Ito differential of the discounted portfolio can lead you to the strategy (just take a look on the martingale term).
May
17
comment Desired portfolio volume
thanks, I'll try and get back to you.
May
17
comment Desired portfolio volume
thanks a lot for the answer, however I am more interested in case when the capital $X$ matters. Shall I look into power utility functions?
May
17
comment Desired portfolio volume
@quasi: I am not very familiar with utility theory, so can you elaborate on how to apply your advice?
May
17
asked Desired portfolio volume
May
17
comment How to prove that markets are incomplete under the Stochastic Volatility model?
It might have been discussed in "Foundation of Stochastic Financial Mathematics" by A. Shiryaev
Apr
25
comment Is statistical arbitrage on FX possible?
@maximus_m: google Modern Portfolio theory, and start with a wikipedia page. Also, depending on your technical affinity, you may want to check out that book
Feb
28
awarded  Popular Question
Feb
21
awarded  Yearling