We would like to thank a former student Ong Bi-Hui at the National University of Singapore for obtaining preliminary results on this problem. We are thankful to the co-editor, Jerome Detemple and two anonymous referees for valuable suggestions on how to improve the paper. The research of M.S. was partially supported by NUS academic research grant R-314-000-068-122. The research was done while J.U. was a student in the Computational Engineering Programme, Singapore-MIT Alliance, National University of Singapore, Singapore 117576.
TRACTABLE ROBUST EXPECTED UTILITY AND RISK MODELS FOR PORTFOLIO OPTIMIZATION
Article first published online: 22 SEP 2010
© 2010 Wiley Periodicals, Inc.
Volume 20, Issue 4, pages 695–731, October 2010
How to Cite
Natarajan, K., Sim, M. and Uichanco, J. (2010), TRACTABLE ROBUST EXPECTED UTILITY AND RISK MODELS FOR PORTFOLIO OPTIMIZATION. Mathematical Finance, 20: 695–731. doi: 10.1111/j.1467-9965.2010.00417.x
- Issue published online: 22 SEP 2010
- Article first published online: 22 SEP 2010
- Manuscript received March 2008; final revision received January 2009.
- robust portfolio optimization;
- expected utility;
- conic programming
Expected utility models in portfolio optimization are based on the assumption of complete knowledge of the distribution of random returns. In this paper, we relax this assumption to the knowledge of only the mean, covariance, and support information. No additional restrictions on the type of distribution such as normality is made. The investor’s utility is modeled as a piecewise-linear concave function. We derive exact and approximate optimal trading strategies for a robust (maximin) expected utility model, where the investor maximizes his worst-case expected utility over a set of ambiguous distributions. The optimal portfolios are identified using a tractable conic programming approach. Extensions of the model to capture asymmetry using partitioned statistics information and box-type uncertainty in the mean and covariance matrix are provided. Using the optimized certainty equivalent framework, we provide connections of our results with robust or ambiguous convex risk measures, in which the investor minimizes his worst-case risk under distributional ambiguity. New closed-form results for the worst-case optimized certainty equivalent risk measures and optimal portfolios are provided for two- and three-piece utility functions. For more complicated utility functions, computational experiments indicate that such robust approaches can provide good trading strategies in financial markets.