A Problem For Optimal Security Portfolio And Consumption Choice

This dissertation studies an optimal security portfolio and consumption choice problem. First, by equilibrium of supply and demand this dissertation shows that the optimal security portfolio and consumption choice always exists in the single-period economic system. And then, from a simple example, the dissertation studies the problem in the multi-period economic system by dynamic program principle in discrete time and continuous time. What' s more, in this part, it illustrates the algorithm by the examples. Finally, for the complexity of the dynamic programming, this dissertation shows a newalgorithm- approximation value function to solve the problem numerically.The algorithm is parsimonious and is first illustrated by solving two examples, first, the standard Merton problem, and second, jump diffusion problem. The algorithm works well, and it has several benefits. First, it may be used to handle higher-dimensional problems without solving a high-dimensional differential function. Second, the complexity of form of the value functional V( θ Aloes not impact substantially the computational requirements of the algorithm. Third the number of points in the state space U does, however, increase the number of constraints to be satisfied. But this was not found to be numerically difficult.