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 Oct9 comment Show that $E[B_t|\mathscr{F}_s] = B_s$ Yep, totally correct. Oct9 comment Show that $E[B_t|\mathscr{F}_s] = B_s$ Technical point: the pde condition on f only guarantees that it will be a local martingale. Integrability has to be checked separately. May22 comment Existence of a hedging portfolio and martingale property ok, so the supermartingale is the value process corresponding to an american option. if i understand your question, then at a theoretical level, the answer is yes: doob-meyer decomposition to split the supermartingale into a martingale and decreasing process, and then martingale representation to get a hedging strategy for the martingale part. May22 comment Existence of a hedging portfolio and martingale property what do you mean by a super martingale price process? May18 comment Difference betweem martingale property and adapted filteration Also, this is something I think about from time to time. You can definite martingality intrinsically, by taking the filtration to be the natural one generated by $X$. Does this mean that martingality is an intrinsic property? May18 comment Difference betweem martingale property and adapted filteration Continuity and measurability are defined slightly differently than what you said. For a continuous function, inverse image of an open set is open, and similarly with measurable. If you unpack the $\epsilon-\delta$ definition of continuity, you'll see that this is what it's logically equivalent to. Apr22 comment Distribution of Brownian Bridge The starting point doesn't matter. You're conditioning on the Brownian Motion being $a$ at time $T_1$, so there's no variance there. Just do the calculation on $[0, T_2 - T_1]$. Apr9 comment unique equivalent martingale measure in incomplete markets yeah. you apply $f(x)$ pointwise. Apr8 comment unique equivalent martingale measure in incomplete markets yeah, thanks. this was a while ago, i have to try and understand what i wrote. Apr8 comment How can the Wiener process be nowhere differentiable but still continuous? Continuity is a weaker property than differentiability. Apr8 comment How do you calibrate a poisson arrival rate process? Don't you know $\delta$? You have to estimate $A$, where $A \leq 1$? Mar31 comment backward Kolmogorov equations - Markov properties Answer below looks correct to me. Also, it doesn't make sense to say that $a$ and $b$ are ito-integrable, as they're just real-valued functions. Mar24 comment Definition of orthogonality and independence for a stochastic processes I've spent quality time with all of these. Williams: Probability w/ Martingales, Oksendahl, Karatzas/Shreve, Protter: Stochastic Integration, Revuz/Yor: Continuous Martingales and BM, Kallenberg: Foundations of Modern Probability Mar24 comment Definition of orthogonality and independence for a stochastic processes I'm not sure where I learned them, that's just how I remember them. I think they're both pretty standard. Mar23 comment Definition of orthogonality and independence for a stochastic processes Yeah if you had the filtration defined already you would do that. Mar18 comment Places to make quant code/tools publicly avaliable you can also use bitbucket for a free private repository. at github you only get public for free. Mar14 comment Places to make quant code/tools publicly avaliable is github too general? Mar7 comment Wiener process proof The question could use a little rewording. You should define what "eventually equates" means. Anyway, I think the point is that the drift term decays at a faster rate than the volatility. Feb28 comment The concept of an incomplete market I don't remember the exact source, but I think Duffie wrote a nice paper (maybe the original one?) on Arrow-Debreu securities and equilibria in an incomplete market. Feb27 comment What is the necessary level of Econometrics-Know-How for a quant Thanks for this answer!