TY - JOUR
T1 - Optimality conditions in portfolio analysis with general deviation measures
AU - Rockafellar, R. Tyrrell
AU - Uryasev, Stan
AU - Zabarankin, Michael
PY - 2006/7
Y1 - 2006/7
N2 - 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.
AB - 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.
KW - CAPM-like relations
KW - Conditional value-at-risk
KW - General deviation measures
KW - Generalized master funds
KW - Optimality conditions
KW - Portfolio analysis
KW - Risk envelopes
KW - Risk identifiers
KW - Risk management
KW - Stochastic optimization
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U2 - 10.1007/s10107-006-0721-9
DO - 10.1007/s10107-006-0721-9
M3 - Article
AN - SCOPUS:33745712297
SN - 0025-5610
VL - 108
SP - 515
EP - 540
JO - Mathematical Programming
JF - Mathematical Programming
IS - 2-3
ER -