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by Alan
Today, 3:21 pm
Forum: General Forum
Topic: Philosophy of Mathematics
Replies: 171
Views: 20354

Re: Philosophy of Mathematics

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...
by Alan
November 17th, 2018, 5:05 am
Forum: Student Forum
Topic: Silly questions
Replies: 57
Views: 2581

Re: Silly questions

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 [$]x = \log S[$] ...
by Alan
November 11th, 2018, 11:35 pm
Forum: Off Topic
Topic: California: Here comes Ahnoooold!
Replies: 225
Views: 200557

Re: California: Here comes Ahnoooold!

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

Image
An owl sits on Zuma Beach as fire moves through the mountains into Malibu. (Wally Skalij / Los Angeles Times)
by Alan
November 10th, 2018, 7:44 pm
Forum: Technical Forum
Topic: Need a proof (GARCH related)
Replies: 13
Views: 311

Re: Need a proof (GARCH related)

@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!
by Alan
November 10th, 2018, 5:45 pm
Forum: Technical Forum
Topic: Need a proof (GARCH related)
Replies: 13
Views: 311

Need a proof (GARCH related)

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...
by Alan
November 10th, 2018, 5:58 am
Forum: Off Topic
Topic: California: Here comes Ahnoooold!
Replies: 225
Views: 200557

Re: California: Here comes Ahnoooold!

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...
by Alan
November 9th, 2018, 2:59 pm
Forum: General Forum
Topic: MBS and Negative Duration
Replies: 1
Views: 114

Re: MBS and Negative Duration

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...
by Alan
November 9th, 2018, 6:11 am
Forum: Student Forum
Topic: Opinion on selecting Module Electives for Bachelor's Degree
Replies: 8
Views: 205

Re: Opinion on selecting Module Electives for Bachelor's Degree

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...
by Alan
October 31st, 2018, 12:56 am
Forum: Politics Forum
Topic: Trump -- the last 100 days
Replies: 2220
Views: 47394

Re: Trump -- the last 100 days

Well, I have to admit that I learned a new word (dicta).
by Alan
October 30th, 2018, 7:18 pm
Forum: Politics Forum
Topic: Trump -- the last 100 days
Replies: 2220
Views: 47394

Re: Trump -- the last 100 days

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 ...
by Alan
October 30th, 2018, 12:07 am
Forum: General Forum
Topic: Formal verification of math finance.
Replies: 3
Views: 529

Re: Formal verification of math finance.

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...
by Alan
October 29th, 2018, 5:32 pm
Forum: General Forum
Topic: Formal verification of math finance.
Replies: 3
Views: 529

Re: Formal verification of math finance.

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...
by Alan
October 26th, 2018, 3:18 am
Forum: Off Topic
Topic: Amundsen Calling - Antarctica
Replies: 63
Views: 6949

Re: Amundsen Calling - Antarctica

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

Image
by Alan
October 22nd, 2018, 10:05 pm
Forum: Off Topic
Topic: Melodic Metal
Replies: 265
Views: 20862

Re: Melodic Metal

"I am Satchmo, Destroyer of Wonderful Worlds."
Well, in that case, Shakira covers Metallica:
by Alan
October 19th, 2018, 7:49 pm
Forum: Trading Forum
Topic: Tools for becoming a great trader
Replies: 10
Views: 2483

Re: Tools for becoming a great trader

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.  
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