Ito process as numerical solution of stochastic differential equation

[yizhang]

@betanalpha

In general a single realization of a stochastic process won’t be differentiable with respect to the input parameters, hence an ensemble of realizations won’t be either. Conditioning on the stochasticity (i.e. passing in precomputed PRNGs) offers one workaround, as the conditional paths might then be smoothly related to the input parameters.

Sounds like you are referring the pathwise sensitivies when calculating greeks in finance, and the rationale can be found, for example, http://www.columbia.edu/~mh2078/MonteCarlo/MCS_Greeks.pdf section 2.

@betanalpha

Ultimately because of lack of expertise on these topics within the typical dev community I think we would all benefit from a bit more doc in order to better understand the approach instead of having to deconvolve the method from the code itself.

Good point, I’ll write more doc on this.