Distributionally Robust Mean-CVaR Portfolio Optimization with Cardinality Constraint

For a mean-CVaR model with cardinality constraint, we consider the situation where the true distribution of underlying uncertainty is unknown. We develop a distributionally robust mean-CVaR model with cardinality constraint (DRMCC) and construct the ambiguity set by moment information. We propose a discretization approximation to the moment-based ambiguity set and present the stability analysis of the optimal values and optimal solutions of the resulting discrete optimization problems as the sample size increases. We reformulate the DRMCC model as a bilevel optimization problem. Moreover, we propose a modified bilevel cutting-plane algorithm to solve the DRMCC model. Finally, some preliminary numerical test results are reported. We give the in-sample performance and out-of-sample performance of the DRMCC model.