Maximization problem in a Stochastic two-country-economy using exchange rates

In this work, it has been studied the maximization problem of expected utility function for a financial agents who invest in a stochastic capital asset pricing model of two-country-economy (a domestic and a foreign markets). The starting points are using the spot and forward exchange rates (as key variables for obtaining new insight on investors' behavior), a seminal Karatazas et al.'s paper and the results achieved by Basak&Gallmeyer and Chiarolla&Haussmann. The idea is considering a more realistic framework, in which the agents can consume not only domestic good but the foreign one too. The relevant tools are stochastic optimization and martingale property, which can give a useful link of microeconomics to macroeconomics, for a general equilibrium structure.