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May
18
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?
May
18
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.
May
18
answered Difference betweem martingale property and adapted filteration
May
3
awarded  Custodian
May
3
reviewed No Action Needed What is the hedging underlying of MBS
Apr
22
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 $[0, T_2 - T_1]$.
Apr
9
comment unique equivalent martingale measure in incomplete markets
yeah. you apply $f(x)$ pointwise.
Apr
8
revised unique equivalent martingale measure in incomplete markets
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Apr
8
comment unique equivalent martingale measure in incomplete markets
yeah, thanks. this was a while ago, i have to try and understand what i wrote.
Apr
8
comment How can the Wiener process be nowhere differentiable but still continuous?
Continuity is a weaker property than differentiability.
Apr
8
comment How do you calibrate a poisson arrival rate process?
Don't you know $\delta$? You have to estimate $A$, where $A \leq 1$?
Apr
7
answered Simple question about expected value of brownian motion
Apr
5
reviewed Reject Are e-mini markets manipulated?
Mar
31
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.
Mar
27
revised Does risk-neutral measure have anything to deal with risk-neutrality in utility theory?
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Mar
27
revised Does risk-neutral measure have anything to deal with risk-neutrality in utility theory?
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Mar
26
answered Does risk-neutral measure have anything to deal with risk-neutrality in utility theory?
Mar
24
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
Mar
24
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.
Mar
23
revised Definition of orthogonality and independence for a stochastic processes
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