Risk-adjusted probability measures in portfolio optimization with coherent measures of risk

Naomi Miller, Andrzej Ruszczyński

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


We consider the problem of optimizing a portfolio of n assets, whose returns are described by a joint discrete distribution. We formulate the mean-risk model, using as risk functionals the semideviation, deviation from quantile, and spectral risk measures. Using the modern theory of measures of risk, we derive an equivalent representation of the portfolio problem as a zero-sum matrix game, and we provide ways to solve it by convex optimization techniques. In this way, we reconstruct new probability measures which constitute part of the saddle point of the game. These risk-adjusted measures always exist, irrespective of the completeness of the market. We provide an illustrative example, in which we derive these measures in a universe of 200 assets and we use them to evaluate the market portfolio and optimal risk-averse portfolios.

Original languageEnglish (US)
Pages (from-to)193-206
Number of pages14
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - Nov 16 2008

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


  • Portfolio optimization
  • Risk

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