عنوان مقاله [English]
In this paper, we develop a robust model for the portfolio selection problem under uncertainty conditions. We construct a robust model, whose risk measure is weighted conditional value at-risk (WCVaR). WCVaR is a combination
of the conditional value at-risk (CVaR) with several tolerance levels. We use combinations of the conditional value at-risk (CVaR) measures to get some approximations of the tail Ginis mean difference, with the advantage of being
computationally much simpler than the Ginis measure itself.The studied model is SSD consistent and LP computable. In stochastic dominance, uncertain returns (modeled as random variable) are compared by the point wise
comparison of some performance functions constructed from their distribution functions. The first performance function is defined as the right-continuous cumulative distribution function, and it defines first degree stochastic
dominance (FSD). The second function is derived from the first, and it defines second degree stochastic dominance (SSD). WCVaR is a safety measure with uncertain returns. To handle the parameter uncertainty problem, there is a
recent research trend in the development of new robust optimization approaches. Traditional optimization methods require full knowledge of parameters to allow transformation to a stochastic program. From full information, assumptions of parameters following specific known distributions can sometimes be too strong and their validity criticized. The last approach of robust optimization proposes a robust formulation that is linear, applicable, deterministically solvable, and extendable to discrete optimization without the loss of feasibility of solution. Another advantage of the model is its ease in controlling the level of conservatism. In this paper, we apply this approach
and develop the robust weighted conditional value at-risk in a portfolio selection problem. We also show the performance of robust optimization in the flexibility of financial markets.