收益率椭球分布不确定下的均值-CVaR优化研究

Worst-Case Optimization on Mean-CVaR Ratio with Returns Distribution Ellipsoidal Uncertainty

The article explores a mean-CVaR ratio model with returns distribution uncertainty.To describe the uncertainty of returns distribution,a mixture ellipsoidal distribution absorbing some typical distributions such as the mixture distribution and and ellipsoidal distribution is introduced.Then,by using robust technique with some assumptions,the original robust mean-CVaR ratio model can be formulated as a second-order cone optimization model where the underlying random returns have a mixture ellipsoidal distribution.As an illustration,the corresponding robust optimization models are applied to allocations of assets in securities market.Numerical simulations are presented to illustrate the relation between robustness and optimality and to compare mixture ellipsoidal distribution to some typical distributions as well.