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Solving Nonlinear Portfolio Optimization Problems with the Primal-Dual Interior Point Method

Jacek Gondzio (J.Gondzio***at***ed.ac.uk)
Andreas Grothey (A.Grothey***at***ed.ac.uk)

Abstract: Stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning. The deterministic equivalent formulations of these stochastic programs have huge dimensions even for moderate numbers of assets, time stages and scenarios per time stage. So far models treated by mathematical programming approaches have been limited to simple linear or quadratic models due to the inability of currently available solvers to solve NLP problems of typical sizes. However stochastic programming problems are highly structured. The key to the efficient solution of such problems is therefore the ability to exploit their structure. Interior point methods are well-suited to the solution of very large nonlinear optimization problems. In this paper we exploit this feature and show how portfolio optimization problems with sizes measured in millions of constraints and decision variables, featuring constraints on semi-variance, skewness or nonlinear utility functions in the objective, can be solved with the state-of-the-art solver.

Keywords: Nonlinear Programming, Portfolio Optimization, Interior Point Methods, Parallel Computing

Category 1: Nonlinear Optimization

Category 2: Applications -- OR and Management Sciences (Finance and Economics )

Category 3: Stochastic Programming

Citation: Technical Report MS 2004-001, School of Mathematics, Edinburgh University, Edinburgh EH9 3JZ, UK March 2004

Download: [Postscript][Compressed Postscript][PDF]

Entry Submitted: 04/02/2004
Entry Accepted: 04/02/2004
Entry Last Modified: 04/02/2004

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