riotburn
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 Mar20 awarded Popular Question Jun10 awarded Popular Question Jul8 comment Solving a system of non-linear (trig) equations: What does your third equation equal? Are your unknowns the three greeks or is it the three greeks and A? If its four unknowns then you have to use a trig identity to get the fourth equation. May23 comment How do you make dependent Brownian motions independent? so are you saying that dB(t) multiplied by the inverse of the correlation matrix on left hand side is independent? May23 asked How do you make dependent Brownian motions independent? Apr11 comment Can someone explain to me Feyman Kac and walk through an example? This is great, thanks Apr11 accepted Can someone explain to me Feyman Kac and walk through an example? Apr11 asked Can someone explain to me Feyman Kac and walk through an example? Dec20 comment How do you show this is a martingale? Yup you're right, I must be stupid or something then. Goodnight! Dec20 comment How do you show this is a martingale? thanks for your help but I fail to grasp why you fail to grasp that someone asking for help on a math help forum is having trouble with a math question... Dec20 comment How do you show this is a martingale? $\int e^{\sigma (x-y)} \frac{1}{\sqrt {2 \pi (t-s)}} e^{-\frac{(x-y)^2}{2(t-s)} }dy$ ? Honestly not sure, the exponential is throwing me off. Dec20 comment How do you show this is a martingale? Ok so its normally distributed with mean 0 and var t-s. How do you solve $E[e^{\sigma (B(t) - B(s))}]$? Dec20 awarded Student Dec20 asked How do you show this is a martingale? Dec19 comment Expectation of Stopping Time w.r.t a Brownian Motion You just blew my mind. Thank you so much! Dec19 awarded Scholar Dec19 accepted Expectation of Stopping Time w.r.t a Brownian Motion Dec19 comment Expectation of Stopping Time w.r.t a Brownian Motion Thank you for the answer! The first part this question comes from asks to prove that $(B^2_t - t)$ is a martingale. I never made the connection nor what the usefulness of the stopping theorem was. Two questions. How do you get $P(B_{\tau}=-a) = 1 - P(B_{\tau})$? How do you get $P(B_{\tau}=b)$? Dec19 comment Expectation of Stopping Time w.r.t a Brownian Motion I'm looking how to solve $E(\tau )$ in general. The stopping time defined in the original question is a practice question for my final. Dec19 comment Expectation of Stopping Time w.r.t a Brownian Motion Using M as any martingale such that the optional stopping theorem states: Let $\tau$ be a stopping time and $M_n$ be a martingale. If there is $K\in \mathbb(N)$ such that $\tau \le K$ almost surely then $E(M_{\tau})=E(M_0)$.