Optimality conditions in portfolio analysis with general deviation measures

R. Tyrrell Rockafellar, Stan Uryasev, Michael Zabarankin

Research output: Contribution to journalArticlepeer-review

69 Scopus citations

Abstract

Optimality conditions are derived for problems of minimizing a general measure of deviation of a random variable, with special attention to situations where the random variable could be the rate of return from a portfolio of financial instruments. General measures of deviation go beyond standard deviation in satisfying axioms that do not demand symmetry between ups and downs. The optimality conditions are applied to characterize the generalized ''master funds'' which elsewhere have been developed in extending classical portfolio theory beyond the case of standard deviation. The consequences are worked out for deviation based on conditional value-at-risk and its variants, in particular.

Original languageEnglish
Pages (from-to)515-540
Number of pages26
JournalMathematical Programming
Volume108
Issue number2-3
DOIs
StatePublished - Jul 2006

Keywords

  • CAPM-like relations
  • Conditional value-at-risk
  • General deviation measures
  • Generalized master funds
  • Optimality conditions
  • Portfolio analysis
  • Risk envelopes
  • Risk identifiers
  • Risk management
  • Stochastic optimization

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