Essays on numerical solution methods, incomplete markets and international business cycle

Models with incomplete asset markets have long been used in the literature on portfolio allocation and precautionary savings. In the 1990s, incomplete markets models also became popular in the real business cycle literature. The failure of the basic model of international real business cycles ( IRBC) to reproduce the low cross-country correlation of consumption sparked interest in IRBC models with incomplete asset markets.;Firstly, this thesis examines the accuracy of the log-linearisation method commonly used to solve IRBC models with exogenous incomplete markets. The analysis finds that the parametrisations of the stochastic process for the productivity shocks which address the cross-country consumption correlation puzzle are precisely those where numerical solutions may be least accurate. Therefore, different models or solution methods will be necessary if we want to identify the economic effect of imposing restrictions on the asset markets.;Secondly, an alternative numerical solution method, dynamic programming by the generalised method of moments (DP by GMM) is presented. One advantage of this solution method is that it does not require a complete knowledge of the stochastic processes for the exogenous variables. DP by GMM will therefore prove useful in solving models whose predictions depend on the parametrisation of the stochastic processes for the exogenous variables. This solution method is employed to solve a joint portfolio allocation and precautionary savings model. Numerical integration and special cases of this model with known analytical solutions are used to show that the solution method is accurate.;Finally, drawing on the previous results, a dynamic model of a small-open economy is solved by DP by GMM. The historical paths for the exogenous variables, measured using Canadian data, are used directly in the solution method. The model is found to predict well the dynamics in the historical paths for output, consumption, investment and the trade balance. The model is also found to generate a predicted trade balance path that is as volatile as the historical path.