Implementable algorithms for stochastic nonlinear programs with applications to portfolio selection and revision

This dissertation has two main objectives: first, to develop efficient algorithms for the solution of one and two period constrained optimization problems, and second, to apply these methods to the solution of portfolio selection and revision problems. The algorithms developed are based upon the Frank-Wolfe method. A convergent algorithm is developed which modifies this approach to allow for sequences of approximations to the objective and to the gradient of the objective, as well as inexact linear searches. By utilizing varying degrees of accuracy (with increasing precision as the optimum is approached), the method will be computationally more tractable than fixed tolerance methods without sacrificing the convergence properties. This algorithm is then applied to a static portfolio selection problem. Here the investor has a wealth allotment to be allocated to a number of possible risky investments with the objective of maximizing the expected utility of terminal wealth. The investor's preferences are assumed to be given by a (von-Neumann-Morgenstern) utility function. For the empirical studies seven classes of utility functions and ten joint normally distributed assets are used. One question investigated is the degree to which the Arrow-Pratt risk aversion measure determines portfolio composition. The empirical results are augmented by a theorem showing (for normally distributed security returns) that the Rubinstein global risk aversion measure is sufficient to determine portfolio composition. The second part of this dissertation deals with two period problems. An algorithm, based on the method of Hogan for extremal value functions, is developed. The extensions (and subsequent advantages) are analogous to those developed for the one period problem. This method is used to solve a portfolio revision problem utilizing five joint normally distributed assets and proportional transaction costs. Empirically, it is shown that significant errors are generated by ignoring the revision aspect of the problem, even with serially uncorrelated returns.Business, Sauder School ofGraduat