4 ms·

Banks do that all the time with monte carlo simulation. Can't get a closed form solution? Simulate every possible outcome and aggregate them.

filmor 6y ago
This is neither how a Monte-Carlo process works (it's sampling the possible outcomes randomly, not simulating all outcomes), nor what is described here (building a physical system where an observable value is described by the differential equation one is trying to solve).
- curiousgal 6y ago
  In practice the number of simulated scenarii is quite large which is what I meant by "every". Not rigorous though, I concur. Monte Carlo methods are used to solve partial differential equations, I found both approaches similar in the sense that they look at how the system actually/could behave, instead of looking at the equations solely.
- stagehn 6y ago
  This is a pedantic response. There isn't an important difference between building a physical system and building a system in code whose generating process is that which you're trying to model. And everyone knew he didn't mean every outcome literally.
CPLX 6y ago
You’re talking more about goal-seeking functions right? That’s the one I always see in a finance context.
seanhunter 6y ago
Worked in the securities division of a leading investment bank for 8 years including on the equities exotics and hybrids trading desk. And I can confirm that we used to use MC whenever we had something we couldn't price using a closed form method. That said, it's a lot slower and more compute intensive so when you could use a grid pricer or pde solver or whatever people would use that instead. You're not really simulating every outcome, just a "large enough" representative sample. As an aside, my dad was a chemical engineer and Newton-Raphson was his equivalent everything-is-a-nail numerical method. We used to use brent root and monte carlo simulation in the same way. Numerical methods are awesome in general.
brewmarche 6y ago
There is actually even a connection between PDEs and SDEs (stochastic differential equations), namely the Feynman-Kac formula which is used a lot in financial mathematics, but it generally allows you to switch between the expectation operator and solving a PDE.

filmor 6y ago

This is neither how a Monte-Carlo process works (it's sampling the possible outcomes randomly, not simulating all outcomes), nor what is described here (building a physical system where an observable value is described by the differential equation one is trying to solve).

curiousgal 6y ago
In practice the number of simulated scenarii is quite large which is what I meant by "every". Not rigorous though, I concur. Monte Carlo methods are used to solve partial differential equations, I found both approaches similar in the sense that they look at how the system actually/could behave, instead of looking at the equations solely.
stagehn 6y ago
This is a pedantic response. There isn't an important difference between building a physical system and building a system in code whose generating process is that which you're trying to model. And everyone knew he didn't mean every outcome literally.

CPLX 6y ago

You’re talking more about goal-seeking functions right? That’s the one I always see in a finance context.

seanhunter 6y ago

Worked in the securities division of a leading investment bank for 8 years including on the equities exotics and hybrids trading desk. And I can confirm that we used to use MC whenever we had something we couldn't price using a closed form method. That said, it's a lot slower and more compute intensive so when you could use a grid pricer or pde solver or whatever people would use that instead. You're not really simulating every outcome, just a "large enough" representative sample. As an aside, my dad was a chemical engineer and Newton-Raphson was his equivalent everything-is-a-nail numerical method. We used to use brent root and monte carlo simulation in the same way. Numerical methods are awesome in general.

brewmarche 6y ago

There is actually even a connection between PDEs and SDEs (stochastic differential equations), namely the Feynman-Kac formula which is used a lot in financial mathematics, but it generally allows you to switch between the expectation operator and solving a PDE.