It would have taken me no time at all to not bother replying.

Did you actually read those links? "In

applied mathematics, the

**curse of dimensionality** refers to the fact that some problems become

intractable as the number of the variables increases"

I don't mean to be short with you, but I mean, I googled your own original question "dimensionality of a pricing problem" and get plenty hits.

See:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.83.8557&rep=rep1&type=pdf
"Many problems in mathematical finance can be formulated as highdimensional

integrals, where the large number of dimensions arises from small time

steps in time discretization and/or a large number of state variables."

Or alternatively:

http://www.smp.uq.edu.au/content/lifting-curse-dimensionality
“High dimensional problems, that is,

**problems with a very large number of variables**, are coming to play an ever more important role in applications. These include, for example, option pricing problems in mathematical finance, maximum likelihood problems in statistics, and porous flow problems in computational physics.”

Go back and read the wiki article on the curse again. Particularly the comparison of sampling a line, versus a hypercube. It is my impression that it may be helpful think of your problem in terms of geometric dimensions.. a dimension is an axis, (a variable, along which some value may be observed, ala an axis, NOT a data point representing an actual observation, ala your 30 days daily obs).

Side note: I do not believe that the variables must be stochastic in nature. And unless I'm wildly mistaken, your single geo original example would be a 1 dimension (assuming your brownian motion is a standard 1D brownian motion and is the only variable driving the prices)

Pleasant reading.

(Slightly apology. Bad day at work.)