How to handle factorial or factorial-alike form?

I wonder how a factorial or a factorial-alike form could be handled with Dynare.

Just for simplicity, an example is as follows.

x(t)=(1+1/1)(1+1/2)…* (1+1/t)

I have attempted to transform the factorial into


In recursive form: log(x(t))=log(x(t-1))+log(1+1/t)

In Dynare


However, log(1+1/t) is a bit problematic, as t is introduced as a new variable and denotes the same time period to which y and x refer. Besides, I don’t know how to assign an initial/a steady state value to the new variable t. How to deal with the scale of t is also a issue.

Thank you for your advance and tips!

I am not sure, Dynare can handle such a setup. Dynare uses local solutions by approximation the decision rules around a well-defined steady state. In your case, I am not even sure such a steady state exists due to the trend in t.