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I have been reading about natural filtrations, and I think I have a good grasp of them. However, I also found out that natural filtrations are just one type of filtration in general. Now I am not able to imagine a filtration other than a natural filtration which would serve a purpose.

So the question is, how does a filtration generalize the idea of a natural filtration, and in particular, where would I use a filtration which is not a natural filtration.

(For context, I am studying valuation of derivative contracts, and they are obviously riddled with natural filtrations.)

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  • $\begingroup$ I had ta similar question as you and see that this one still does not have an answer. My question has received and answer: math.stackexchange.com/questions/4503078/…. $\endgroup$ Jul 31, 2022 at 16:00
  • $\begingroup$ It would seem to me that we always see natural filtrations for the following reason. Stochastic processes generate its natural filtration. When constructing an example of a filtration we always think of how the stochastic process evolves such as up and down movement in the binomial lattice model for derivatives. Hence, we will be doomed to constructing the natural filtration. The answer to my question stated multi-dimensional Brownian motion to have a filtration which is not the natural filtration of the uni-variate Brownian motions. $\endgroup$ Jul 31, 2022 at 16:04

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