Robust portfolio selection based on a multi-stage scenario tree

Ruijun Shen, Shuzhong Zhang

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


The aim of this paper is to apply the concept of robust optimization introduced by Bel-Tal and Nemirovski to the portfolio selection problems based on multi-stage scenario trees. The objective of our portfolio selection is to maximize an expected utility function value (or equivalently, to minimize an expected disutility function value) as in a classical stochastic programming problem, except that we allow for ambiguities to exist in the probability distributions along the scenario tree. We show that such a problem can be formulated as a finite convex program in the conic form, on which general convex optimization techniques can be applied. In particular, if there is no short-selling, and the disutility function takes the form of semi-variance downside risk, and all the parameter ambiguity sets are ellipsoidal, then the problem becomes a second order cone program, thus tractable. We use SeDuMi to solve the resulting robust portfolio selection problem, and the simulation results show that the robust consideration helps to reduce the variability of the optimal values caused by the parameter ambiguity.

Original languageEnglish (US)
Pages (from-to)864-887
Number of pages24
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - Dec 16 2008

Bibliographical note

Funding Information:
Research supported by Hong Kong RGC Earmarked Grants, CUHK4174/03E and CUHK4242/04E.


  • Conic optimization
  • Portfolio selection
  • Robust optimization
  • Scenario tree


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