r**a
发帖数: 536 | 1 How do we know a numerical solution of a SDE gotten by using monte carlo
simulation is
reliable? Is this question related to the stability of monte carlo
simulation?
Thanks in advance. | r**a
发帖数: 536 | 2 How do we know a numerical solution of a SDE gotten by using monte carlo
simulation is
reliable? Is this question related to the stability of monte carlo
simulation?
Thanks in advance. | L*******t
发帖数: 2385 | 3 I guess one should obtain convergence result first. at least for those
discretization schemes. It's required by many numerical schemes...
For example, Takahashi and Fujii proposed many series expansion solutions to
FBSDE's, but they did not post any convergence results until recently. What
they did back then was just to compare their methods with the closed form
solutions of some FBSDE's, and claimed their methods worked, but they also
wrote a sentence in their paper that they were not responsible for any loss
caused by their methods applied by someone else.
So, Whenever one wishes to apply some numerical schemes to solve SDE or PDE
or something, convergence result is the first thing he should look for.....
【在 r**a 的大作中提到】
: How do we know a numerical solution of a SDE gotten by using monte carlo
: simulation is
: reliable? Is this question related to the stability of monte carlo
: simulation?
: Thanks in advance.
| r**a
发帖数: 536 | 4 Of course, you need to first check the convergence of the numerical scheme
you want to use. But besides the convergence, stability also matters
sometime.
to
What
loss
PDE
【在 L*******t 的大作中提到】
: I guess one should obtain convergence result first. at least for those
: discretization schemes. It's required by many numerical schemes...
: For example, Takahashi and Fujii proposed many series expansion solutions to
: FBSDE's, but they did not post any convergence results until recently. What
: they did back then was just to compare their methods with the closed form
: solutions of some FBSDE's, and claimed their methods worked, but they also
: wrote a sentence in their paper that they were not responsible for any loss
: caused by their methods applied by someone else.
: So, Whenever one wishes to apply some numerical schemes to solve SDE or PDE
: or something, convergence result is the first thing he should look for.....
| r**a
发帖数: 536 | 5 Furthermore, in practice, we often know the moments of the terminal
distribution. i.e. the moments sometime have analytic solution. So, in those
cases, we may test the terminal moments from the sampled process. This may
be able to give us some clues on the reliability of the numerical solutions.
to
What
loss
PDE
【在 L*******t 的大作中提到】
: I guess one should obtain convergence result first. at least for those
: discretization schemes. It's required by many numerical schemes...
: For example, Takahashi and Fujii proposed many series expansion solutions to
: FBSDE's, but they did not post any convergence results until recently. What
: they did back then was just to compare their methods with the closed form
: solutions of some FBSDE's, and claimed their methods worked, but they also
: wrote a sentence in their paper that they were not responsible for any loss
: caused by their methods applied by someone else.
: So, Whenever one wishes to apply some numerical schemes to solve SDE or PDE
: or something, convergence result is the first thing he should look for.....
|
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