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.

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.