We are looking for closed form solution to CMS spread range accruals under 2-factor Hull-White.
Any tips, @DavidJN?

At the very least, closed-forms make great control variates in the cases where numerical methods are required. They are properly viewed as complementary,.

So, they play second fiddle in certain cases?


// He was Russian, not Romanian, I think

In a hotel an engineer, a physicist and a mathematician  are sleeping when a fire breaks out.
 
The engineer wakes up, notices the fire, grabs the next fire extinguisher and starts spraying.... After what seems hours of heroic fighting the fire is gone and he goes to sleep again.
 
But the fire breaks out again. The physicist wakes up, notices the fire, grabs the fire extinguisher .... stares at the fire for some minutes, does some calculations in his head - air flow, humidity, thermodynamic whatever - and then - with one blow from the extinguisher at the right point the fire is out and he goes to sleep again.
 
But the fire breaks out again. The mathematician wakes up, notices the fire, sees the extinguisher - aaaah, the problem is solvable ... and goes to sleep again.

...

The third time the fire does not ignite again. The mathematician notices the smouldering ashes, grabs a book of matches and lights the fire again.. He then goes to sleep satisfied since he has reduced the problem to one that was previously solved.

An old Hacker News comment reveals a surprising insight into Renaissance Technologies' remarkable success: the legendary hedge fund achieved its impressive 66% pre-fee and 39% post-fee annual returns from 1988 to 2018 using a simple regression with one target and one explanatory variable. The comment highlights that the fund's success relied more on having brilliant minds identify the right variables, clean data meticulously, and recognize flawed results than on complex models. This gem challenges the notion that sophistication always trumps simplicity, reminding us that mastering the fundamentals is often the key to exceptional results.

I know a lot of YouTube videos on Jim Simons make a huge point of focusing on hidden Markov with some form of Kelly betting strategy behind it, as Ed Thorpe did as well. I assumed there's a lot more behind it. 

It is true that there is nothing in a stochastic differential equation  that is not in a Fokker-Planck equation, but the stochastic differential equation  is so much easier to write down and manipulate that only an excessively zealous purist would try to eschew the technique.

C.W. Gardiner (2004) Handbook of Stochastic Methods, for Physics, Chemistry and the Natural Sciences, Springer.

Yawn!

The FPE must be one of the finest creations of the human mind, ever.

In order to solve a differential equation you look at it till a solution occurs to you.

George Pólya

"It's really, really important to write your idea out or to draw it out or to code it, but you need to get it out of your head. The reason you have to get it out of your head is you need to be able to see it on a surface that is not in your mind. And once you can see it, and once you can step back from it, then you can also decide if this passes your filter or not" - Jack Dorsey

I've been writing all my equations and algorithms out on paper first (or iPad scribbled onto Noteability). 
Just wanted to get into a more organic way of working before I commit anything to code. 

Arguably, the most important invention ever is Maxwell's electromagnetic PDE equations, eclipsing everything else. They are solved using FEM, FDTD, FDFD, MoM (BEM). 
A myriad of applications, from semiconductors, tracking, telecoms, antenna modelling, EM radiation. The resulting field is called Computational Electromagnetics (CEM). 

With OOP knowledge I reckon some opportunity. And the same FDMs can be used here as well.

Maxwell's PDE does not have an analytical solution.

Infinite series, again.

Mathematician solves algebra’s oldest problem using intriguing new number sequences
https://www.unsw.edu.au/newsroom/news/2 ... -sequences

His new method to solve polynomials also avoids radicals and irrational numbers, relying instead on special extensions of polynomials called ‘power series’, which can have an infinite number of terms with the powers of x. By truncating the power series, Prof. Wildberger says, they were able to extract approximate numerical answers to check that the method worked.

Sounds kind of familiar..