Here's a question on how to overcome the contradiction and incompatibility between Fourier's equation (Fick's Law) and the theory of relativity (in the latter case speed of heat propagation is infinite while in the latter case nothing is faster than light). A fix for this conundrum is to stick a 2n...

Can the method of Separation of Variables be used solve the Black Scholes PDE? 1. If not, why not, where does it break down? 2. If yes, how do you compute a solution? It's an interesting quizzie. There's a lot of maths in there. 2. Yes. Start with the easy driftless BS case, where [$]x = \log S[$] ...

Thanks, ppauper. Here's another photo from the fires:


An owl sits on Zuma Beach as fire moves through the mountains into Malibu. (Wally Skalij / Los Angeles Times)

@bearish,  Thank you: short and sweet!

@ppauper, Thanks, also. Yes, I got this in Mathematica, too, and had plotted it earlier in [$]a+b<1[$], which was why I said that I was numerically convinced.

OK, problem solved -- Thanks again, guys!

Let [$]Z[$] be a standard normal variate. I would like to see a proof that (*) [$]E[\log (a Z^2 +b)] < 0[$] for all [$]\{(a,b): a > 0, b>0, a +b < 1\}[$]. In other words, [$] \int_{-\infty}^{\infty} \log (a z^2 + b) \, e^{-z^2/2} \frac{dz}{\sqrt{2 \pi}} < 0[$] under the same conditions. The connecti...

https://theledgesports.com/wp-content/uploads/2016/12/67dFW5g.jpg There is a *very bad* firestorm ongoing in Malibu & southern Ventura county area of Socal. No deaths or injuries, but 250,000 evacuated and many structures lost so far. Coincidentally, you can see Dolores of my icon standing in front...

Not my area, but the simple answer would be to see if you can characterize a particular tranche as, roughly, "IO-like", "PO-like", or "bond-like". The ones that are more IO-like may have negative duration for the reason you say you understand: rates go up, prepays slow, and you get more cash. More c...

I'd look for a survey course in what's traditionally called "engineering mathematics" that uses, say,  Kreyszig . That combines a bunch of things. Then, add a stochastic calculus course. Plus do Option 2.  Leave the measure theory, functional analysis, etc for grad school.  Other nice things: Mathem...

Well, I have to admit that I learned a new word (dicta).

From today's WSJ: The 1898 Wong Kim Ark case stresses that “subject to the jurisdiction” of the U.S. should be read broadly. “The real object of the 14th Amendment of the Constitution,” the court said, “in qualifying the words, ‘All persons born in the United States’ by the addition ‘and subject to ...

Yes, that can be an issue, although the studies I want to try to replicate for my book use GARCH-type models on broad-based indices like SPX. Also, some authors go out of their way to publish data: I am thinking about, say,  Ken French  or the  Oxford-Man Institute authors .    Anyway, my point is t...

OK, there is a class of models that I use all the time called "GARCH models" (a key inventor, Rob Engle, received the Nobel prize for that). In fact, it is probably one of the most used (and useful!) classes of models in finance. While I have been coding things myself, there is a package in the R sy...

NASA confirms: Aliens are carving rectangular icebergs in Antarctica to mess with us ..

"I am Satchmo, Destroyer of Wonderful Worlds."

Well, in that case, Shakira covers Metallica:

Re news impacts, this is something you can practice. Whenever there is a significant news event, either macro or single-name specific, first guess the impact before looking at the market reaction. Over time, you can learn to ballpark things -- or certainly improve upon where you are now.