I haven’t worked with this type of problems myself, so I am not sure. The typical problem with portfolio choice models is that standard Dynare cannot find the portfolio allocations because it approximates around a deterministic steady state where the portfolio are indeterminate. See the work by Devereux and Sutherland on this.
Regarding Epstein-Zin, see [Expected value of a power). The Caldara et al. (2011) mod-file on my homepage is one example of this.