Tail Gini’s Risk Measures and Related Linear Programming Models for Portfolio Optimization

Several polyhedral risk measures have been recently introduced leading to Linear Programming (LP) models for portfolio optimization. In this paper we study LP solvable portfolio optimization models based on the tail Gini’s mean difference risk measurement. We use combinations of the Conditional Value at Risk (CVaR) measures to get some approximations to the tail Gini’s mean difference with the advantage of being computationally much simpler than the Gini’s measure itself. We introduce the weighted CVaR (WCVaR) measures defined as simple combinations of a very few CVaR measures with specific type of weights settings which relates the WCVaR measure to the tail Gini’s mean difference. This allows us to use a few tolerance levels as only parameters specifying the entire WCVaR measures while the corresponding weights are automatically predefined by the requirements of the corresponding tail Gini’s measure. All the studied models are SSD consistent and LP computable. We analyze both the theoretical properties of the models and their performances on the real-life data.