The purpose of this thesis is to use the martingale approach to solve dynamic international portfolio problems. This thesis consists of three essays in dynamic international portfolio allocation. In demonstrating that foreign consumption plays an important role in international portfolio allocations, in Chapter 2, we present the first essay where we provide the optimal consumption plan and portfolio allocation for a representative investor with continuoustime and complete market assumptions in a simple two-country setting. Due to the demand for foreign consumption, the optimal portfolio allocation requires suitable foreign bonds to hedge against the changes in the foreign investment opportunity set and the exchange rate. The empirical results not only show that the optimal portfolio allocation with domestic and foreign consumption is different from that without consumption or with domestic consumption only, but also demonstrate the need for the foreign bonds to hedge against the change in the exchange rate risk. We present the second essay in which we extend the research of the investor's portfolio allocation problem into a continuous dynamical international market where the investment barrier of international portfolio exists. With deterministic market prices of risks, CRRA utility function and the existence of a simple investment barrier, the investor optimally hedges against the investment opportunity by allocating funds into three portfolios which are constructed by unconstrained bank accounts, equities and bonds. The first portfolio is the so called mean-variance portfolio, the second is the hedge portfolio, and the third is the synthetic portfolio which mimics the expected excess return of the constrained security in foreign country. This issue displays in Chapter 3. The third essay is presented in Chapter 4. Here we develop a continuous-time intertemporal portfolio allocation model in an international mildly segmented market. With deterministic market prices of risks and CRRA utility function, the domestic investor in the segmented market optimally hedges against the stochastic interest rates by allocating funds into two portfolios. The restricted mean-variance portfolio is derived from the traditional mean-variance portfolio without foreign constrained securities. The hedge portfolio is comprised of domestic bonds with a specific horizon for hedging against the change in the domestic interest rate. The numerical results indicate that when the volatility of the stochastic discount factor increases due to the less diversification caused by market segmentation, the less risk-averse investor benefits accordingly. Chapter 5 summarizes the main findings of the three studies and concludes the thesis by suggesting some future research venues related the current subject. / The purpose of this thesis is to use the martingale approach to solve dynamic international portfolio problems. This thesis consists of three essays in dynamic international portfolio allocation. In demonstrating that foreign consumption plays an important role in international portfolio allocations, in Chapter 2, we present the first essay where we provide the optimal consumption plan and portfolio allocation for a representative investor with continuoustime and complete market assumptions in a simple two-country setting. Due to the demand for foreign consumption, the optimal portfolio allocation requires suitable foreign bonds to hedge against the changes in the foreign investment opportunity set and the exchange rate. The empirical results not only show that the optimal portfolio allocation with domestic and foreign consumption is different from that without consumption or with domestic consumption only, but also demonstrate the need for the foreign bonds to hedge against the change in the exchange rate risk. We present the second essay in which we extend the research of the investor's portfolio allocation problem into a continuous dynamical international market where the investment barrier of international portfolio exists. With deterministic market prices of risks, CRRA utility function and the existence of a simple investment barrier, the investor optimally hedges against the investment opportunity by allocating funds into three portfolios which are constructed by unconstrained bank accounts, equities and bonds. The first portfolio is the so called mean-variance portfolio, the second is the hedge portfolio, and the third is the synthetic portfolio which mimics the expected excess return of the constrained security in foreign country. This issue displays in Chapter 3. The third essay is presented in Chapter 4. Here we develop a continuous-time intertemporal portfolio allocation model in an international mildly segmented market. With deterministic market prices of risks and CRRA utility function, the domestic investor in the segmented market optimally hedges against the stochastic interest rates by allocating funds into two portfolios. The restricted mean-variance portfolio is derived from the traditional mean-variance portfolio without foreign constrained securities. The hedge portfolio is comprised of domestic bonds with a specific horizon for hedging against the change in the domestic interest rate. The numerical results indicate that when the volatility of the stochastic discount factor increases due to the less diversification caused by market segmentation, the less risk-averse investor benefits accordingly. Chapter 5 summarizes the main findings of the three studies and concludes the thesis by suggesting some future research venues related the current subject.