Date of Award
Dissertation - Restricted
Doctor of Philosophy (PhD)
Electrical and Computer Engineering
Heinen, James A.
In this study, a continuous time mathematical model is formulated to describe the investment problem: -For a given family and house in which they propose to live or are living, what is the best loan repayment schedule to minimize the total cost of home ownership for the period (O,T)? It is shown that the home investment problem formulated by the model is a generalization of problems presented in the Capital Investment Literature and in Control.Theory, and falls into the category of continuous time stochastic optimal control problems with incomplete state measurements. Approaches to the solution of the optimization problem in the home investment problem are discussed and it is found that the best method of solution is a dynamic programming formulation. The iterative functional equation of dynamic programming for the minimum cost functional is derived for the home investment model. It is shown that the solution to the iterative functional equation exists and is unique and that an optimal repayment schedule .exists. The form of the optimal repayment schedule is also obtained. A method of numerical solution of the iterative functional equation is proposed which is a modified version of the method of Iterative Dynamic Programming which uses the method of feasible directions for solving the nonlinear programming problems in the solution of the iterative functional equation. Theorems on the numerical stability and convergence of solutions to the iterative functional equation are given. A numerical example is solved showing the feasibility of the method, and an optimizing controller is obtained.