Hello everyone,

My question may seem too basic, but now I have wondered about this. It has to deal with transversality conditions.

Reading the Obstfeld and Rogoff textbook *Foundations of International Economics* on this matter, I understand that they always derive their transversality conditions by iterating forward the budget constraint of the representative agent (Chapter 10 for example). Hence, I was trying to follow the same logic, but it seems that the transversality condition I obtained looks way too complicated.

The representative agent supplies labor and capital to intermediate good producing firms, receives real income from wages w_t, a rental return on capital rr_t, and nominal profits from the ownership of firms. The agent then divides its resources to purchase consumption C_t and investment I_t. The agent trades domestic and foreign nominal risk-less bonds B_{H,t} and B_{F,t}.

Hence, the budget constraint the agent faces (under incomplete asset markets) is given by:

\begin{gather} \begin{split} P_t(C_t+I_t)+\frac{B_{H,t}}{1+i_t}+\frac{S_tB_{F,t}}{(1+i^*_t)\Theta\Big(\frac{S_tB_{F,t}}{P_t}\Big)} \leq B_{H,t-1}+S_tB_{F,t-1}+P_tw_tL_t+P_trr_tK_t\\ +\int_0^1\Pi_t(j)dj \end{split} \end{gather}

and capital follows the law of motion K_{t+1} = (1-\delta)K_t + I_t. The cost function \Theta(\cdot) drives a wedge between the return on foreign currency denominated bonds received by domestic and by foreign residents.

I would like to ask for suggestions of paths I could follow to derive the transversality condition considering this budget constraint or if I should adopt a different strategy to derive such condition. A second question is what role the \Theta(\cdot) function would have in the transversality condition as well.

Thank you,

Alejandro