mathematical finance - Matching Dynamic Trading Strategies with Derivatives

I understand your problem is:

(i) You have a time-dependent p&l(I call it pay-off) from trading a portfolio of financial assets (although this doesn't really matter)

(ii) You want to find a static portfolio of assets, replicating this p&l in every state of the world (called the replicating portfolio).

This can be done very easy if:

(a) you work in discrete time, i.e. the pay-off you are trying to match is a finite vector of random variables $G_1$, ..., $G_T$

(b) the pay-off does not depend on the path of the underlying assets you are trading in.

Under these conditions it suffices to find a replicating portfolio at a single time $t$ of pay-off. The pay-off is a real-valued function $f=f(S_t)$ within some function-space and what you really want to do is to approximate $f$ by a set of basis function (i.e. the options).

Of course there are many ways to approximate $f$ as well as many possible choices for basis functions. The best approach will depend on your specific set-up. You have to decide
(A) What function space you are working in: Is piecewise linear OK or will your trading strategy produce discontinuities?
(B) What are your basis instruments? If you are looking for a practical solution you will be restricted to traded instruments, i.e. no far out-of-the money stuff, no digital options and so on.
(C) What is your notion of error? $L^2$ is natural but maybe you have a specific utility or risk aversion?
(D) What is your method of discretizing domain and range of $f$?

Anyway if there are not too many times and underlying assets involved, this might be something simple enough to do in Excel.

On the other hand if condition (b) above is not fulfilled, you are most likely in for some trouble. Path dependency creates lots of problems ("curse of dimension") and from a practical perspective you will have trouble finding sufficiently many path-dependent instruments for replication. The method of choice in that case is a regression approach. I.e. regress the pay-off from your strategy against various instruments you deem appropriate.