Dynamic portfolio management: An approximate linear programming approach
Portfolio management is one of the central subjects of modern finance. However, in most cases it is difficult to determine optimal strategies for intertemporal portfolio management problems. In this thesis, we formulate a class of intertemporal portfolio management problems in the continuous-time framework, and offer a new computational approach, which we call approximate linear programming, to this class of portfolio problems. We start by deriving the corresponding Hamilton-Jacobi-Bellman equation, and transform it into an equivalent linear program. Since this equivalent linear program is intractable due to an infinite number of constraints, we use basis function approximations and constraint-sampling techniques to obtain a tractable approximating linear program. Finally we present efficient algorithms to solve the approximate linear program. Our approximate linear programming approach has four major features: it scales well with dimensions; it has a priori performance bounds; it can deal with both complete and incomplete markets; and it provides an approximate upper bound on the optimal value. We also present case studies to demonstrate the effectiveness of our algorithm, particularly for large portfolios as illustrated in a 10-dimensional problem.
0796: Operations research