Kernel density estimation based distributionally robust mean-CVaR portfolio optimization

In this paper, by using weighted kernel density estimation (KDE) to approximate the continuous probability density function (PDF) of the portfolio loss, and to compute the corresponding approximated Conditional Value-at-Risk (CVaR), a KDE-based distributionally robust mean-CVaR portfolio optimization model is investigated. Its distributional uncertainty set (DUS) is defined indirectly by imposing the constraint on the weights in weighted KDE in terms of phi-divergence function in order that the corresponding infinite-dimensional space of PDF is converted into the finite-dimensional space on the weights. This makes the corresponding distributionally robust optimization (DRO) problem computationally tractable. We also prove that the optimal value and solution set of the KDE-based DRO problem converge to those of the portfolio optimization problem under the true distribution. Primary empirical test results show that the proposed model is meaningful.

Automated summary

This paper investigates a KDE-based distributionally robust mean-CVaR portfolio optimization model by using weighted kernel density estimation to approximate the continuous probability density function of the portfolio loss and compute the corresponding approximated CVaR. The distributional uncertainty set is indirectly defined by imposing a constraint on the weights in weighted KDE, converting the infinite-dimensional space of PDF into a finite-dimensional space. The study proves that the optimal value and solution set of the KDE-based DRO problem converge to those of the portfolio optimization problem under the true distribution. Primary empirical test results show the significance of the proposed model.