We have introduced a general methodology and proved related propositions.
Furthermore, even though applications are not limited to risk management, we have
provided an application of path-wise valuation to risk management.
One of the remaining issues to be addressed would be that we could not enumerate all
the paths when we have many time steps beyond computer abilities such as 100
periods. To resolve this issue, we should pursue how to partition the entire path
space into a manageable number of sub-path space and how to choose the
representative path for each sub-path space. The research direction for this purpose
would be that we have to identify characteristics of a certain option in terms of
path-wise valuation and then find an appropriate measure to collect similar paths.

