Two-country DSGE model: country portfolio and debt

Dear all,

 I am working on a simple DSGE model where two countries with a monetary union interchange debt to optimize consumption in the event of a production shock in one of them. Only the country with shocks issues debt.

 In order to avoid first order indeterminacies (see Devereux-Sutherland country portfolios) I want to introduce a utility function for the country without shocks in a way that consumers like to diversify their investments (i.e. extra utility if investments are distributed between home capital and foreign bonds).

 But until now I couldn't find a suitable function that is stable in the steady state (same interest rate for home capital and foreign bonds to avoid arbitrage).

 More specifically, I introduce logk+logb (k=home capital investments, b=foreign bonds) in the utility function to penalize extreme portfolios (k or b close to 0)
 When applying steady state to the bonds Euler Equation we find the typical result R=1/beta (R being bond interest rate), therefore the Euler Equation of home capital should produce the same interest rate in steady state (same slope of Utility hyperplane with respect to k), for which I am obliged to introduce by hand a term to change the slope (term psi3*k) and tune psi3. I'm not convinced with the method nor the results.

 Any suggestion?

two country debt model 0820.pdf (1.02 MB)
two_country_port_det.mod (1.98 KB)
two_country_port_stoch.mod (1.94 KB)