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 May 24 comment Can I use my powers for good? "And they aren't open to hiring PhDs for entry level jobs (you are "overqualified")." Do you have any evidence to back this claim? A maths PhD I know got 4 job offers in entry-level finance, probably the in the top 5% in terms of success. May 24 comment Can I use my powers for good? How is insurance evil? We need mathematicians to price the extremely hard to price products that wouldn't exist without the talent. Insurance is incredible -- long-term disability insurance, life insurance, the positive impact of these products is far reaching. The evidence that statistical arbitrage is a net harm is not in yet. Some academics view automated market makers (at least) as liquidity providers without which a market can not even exist, and spread traders as aiding in instantaneous cross-asset price discovery. Sell-side quants can build products to help (e.g.)farmers reduce risk May 24 comment Why $\frac{1}{2i}(e^{i\omega t} - e^{-i\omega t}) = \frac{i}{2} (e^{-i \omega t} - e^{i\omega t})$ I get it now thanks guys. Dec 26 comment Black scholes model type @math Here: papers.ssrn.com/sol3/… Dec 13 comment Integral with respect to Wiener process. @did Can you supply the correct answer please? Dec 12 comment Is this geometric Brownian Motion? $\sigma(t)$ is stochastic and has a separate Wiener process inside of it. Dec 4 comment Partial Derivative of an Integral Do you know if/why my answer is incorrect (if yours is correct)? I know that it's false to say that "you can't write partial derivatives w.r.t. BM". For example apply Ito's lemma to the function $f(t,x)$, where $x$ is $B(t)$ (in fact this is one of the most standard routines in stochastic finance). Applying Ito's lemma you will end up having to evaluate $\frac{\partial f}{\partial x}(t,x)$. Dec 4 comment What's the intuition behind non-integer exponents/powers This helps!${}{}{}$ Dec 1 comment Black scholes model type @math I made it ambiguous by skipping a few steps and also dropping the conditional $P\{...|...\}$ notation. Here's what I did: (1) Divide both sides by $S_2(T)$ (doesn't change inequality, GBM is strictly positive), (2) log both sides; $\ln{1} = 0$ so the RHS just becomes 0. Inequality still holds because $ln$ is monotone increasing. Dec 1 comment Black scholes model type @math Unfortunately this is a black box to me (I lifted it from lectures). All I know is that it very very easily allows one to compute the solution to options such as the Magrabe option (which is the one you're asking about). Nov 25 comment Substituting integral into an integral My lecture slides say that the answer is $\displaystyle \ \ \int_0^t \int_u^t \alpha(u,s)dsdu$ Nov 24 comment Density process/Radon-Nikodym derivative problems @DavideGiraudo What you mean by integrating on a set of non-zero measure on which $f \leq 0$. All of that. Nov 24 comment Density process/Radon-Nikodym derivative problems @DavideGiraudo I'm afraid I don't follow. Nov 24 comment Density process/Radon-Nikodym derivative problems @DavideGiraudo I've revised to make this clear. Nov 24 comment The Lebesgue integral $\int_\Omega dP$ @did I'm taking a stochastics course with no background in measure theory so I have holes everywhere, unfortunately! Nov 24 comment Expectation of exponential martingale and indicator function. @did I apologize for the typo. Nov 24 comment Covariation of Wiener processes, $\langle W_1,W_2\rangle_t = \rho t$. @saz No. $\rho$ is the correlation coefficient. The equality $\langle W_1,W_2 \rangle_t = \rho t$ is provided in the (ungraded) homework question's preamble where $\rho \in [-1,1]$. Nov 24 comment Expectation of exponential martingale and indicator function. @TheBridge I am not allowed to change probability measure in this question (they specifically told us so). Nov 23 comment Is it true that $X(t)^a > K \iff X(t) > K^\frac1a$ @Berci Yes. $\phantom{.}$ Nov 22 comment Partial derivative notation: $\left.\frac{\partial \cdot}{\partial\cdot} \right|_{u=T}$ For the first question, why couldn't he have done $\frac{\partial B(t,T)}{\partial T}$, instead of using $u$ and then substituting in $T$ afterwards?