A robust optimization approach to finance

An important issue in real-world optimization problems is how to treat uncertain coefficients. Robust optimization is a modeling methodology that takes a deterministic view: the optimal solution is required to remain feasible for any realization of the uncertain coefficients within prescribed uncertainty sets. The focus of this thesis is on robust linear programming problems in which the uncertainty sets are polytopes. The assumption of polyhedral uncertainty leads to compact, efficiently solvable linear formulations. In the first part of the thesis, we study special types of polyhedral uncertainty sets that allow for incorporating moment information about the distribution of the uncertain coefficients, and for controlling the tradeoff between robustness and optimality. We provide probabilistic guarantees on the feasibility of optimal solutions obtained with such uncertainty sets for any realization of the uncertain coefficients. We then illustrate the versatility of robust polyhedral formulations by studying three financial applications: single period portfolio optimization, multiperiod portfolio management, and credit risk estimation. In the area of single period portfolio optimization, we propose ways of modeling inaccuracy in parameter estimates, and explore the benefits of robust optimal strategies through computational experiments with the statistical estimation of a particular measure of portfolio risk - sample shortfall. We emphasize the advantages of linear, as opposed to nonlinear, robust formulations in large portfolio problems with integrality constraints.

Department dc:contributor.department

Massachusetts Institute of Technology. Operations Research Center.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2002

Author dc:creator

• Pachamanova, Dessislava A. (Dessislava Angelova), 1975-

Advisor dc:contributor.advisor

• Dimitris J. Bertsimas.

• Operations Research Center.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/8509

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/8509