521 reputation
46
bio website
location
age
visits member for 2 years, 1 month
seen 23 hours ago

Dec
10
awarded  Excavator
Dec
10
revised Girsanov theorem in CMS convexity derivation
reformat the brackets in latex.
Dec
10
suggested approved edit on Girsanov theorem in CMS convexity derivation
Dec
9
answered examples of c++ code with application to quant finance
Dec
9
revised Why is this stochastic integral a martingale?
added 4 characters in body
Dec
9
comment Why is this stochastic integral a martingale?
emcor: because of the independent increments property of $W_t$. At time $u$, $S_u$ is known but $dW^*_u \equiv W^*_{u+du}-W^*_u$ is not.
Dec
9
comment Why is this stochastic integral a martingale?
Gordon: correct. I added a section to address the issue.
Dec
9
revised Why is this stochastic integral a martingale?
added 505 characters in body
Dec
9
revised Why is this stochastic integral a martingale?
deleted 2 characters in body
Dec
9
comment Why is this stochastic integral a martingale?
While the OP answered his/her own question, I wonder if he/she just copied the answer from a book. In the OP's answer, it says that it "is possible to show" the lemma that $\int_0^t f(s) dW(s)$ is a martingale, but it "is omitted here to keep things short". What? That's exactly what we are trying to prove!
Dec
9
revised Why is this stochastic integral a martingale?
deleted 12 characters in body
Dec
9
comment Why is this stochastic integral a martingale?
StudentT: exactly! It works out only because $dW_u$ is defined as a forward difference in the Ito integral.
Dec
9
revised Why is this stochastic integral a martingale?
deleted 17 characters in body
Dec
8
comment Why is this stochastic integral a martingale?
Wow my answer is at -1 vote. Folks please go take a Stochastic Calculus class, as this result is fairly basic. Look at slide #12 at idsc.ethz.ch/Courses/stochasticsystems/SDE.pdf; "The expectation of stochastic integrals is zero. This is what we would expect anyway."
Dec
8
comment Why is this stochastic integral a martingale?
fushsialatitude: good question. To move the expectation operator inside the integration, we need to satisfy Fubini's theorem. If $S(u)$ is "well-behavior", the theorem should be satisfied.
Dec
8
revised Why is this stochastic integral a martingale?
edited body
Dec
8
answered Why is this stochastic integral a martingale?
Dec
4
answered Why cant I multiply two SDE Solutions?
Oct
31
awarded  Yearling
Jul
19
revised How to compute $\mathbb{E} \left[ (W_s + W_t - 2W_0)^2 \right]$?
added 57 characters in body