Maybe only those quants who can't program.
The quote was from Jacques Hadamard, e.g. is a PDE 'any good' without trying to find a solution or taking a specific example?
It's a bit like Linnaeus taxonomy stuff or concept hierarchies (superordinate, basic, subordinate). OOP calls it iiheritance.
Example published article double barrier for cash or nothing using SDE A-Z (a lot of hours work, just look eqs. 27, 28!) Reinventing the wheel??
Hadamard would say it's just a PDE with a discontinuous payoff..Instead of always being quantitative ('"chechez closed solution") first examine qualitative properties.
https://www.researchgate.net/profile/Ja ... ion_detail
BTW PDE solver gives same results w/o any modification to the code and no extra maths needed.
// Series solutions are a-posterior accurate (like ANNs) and they may not always converge., With FDM, choose step length h, dt a-priori.