The Mean-CVaR Model for Portfolio Optimization Using a Multi-Objective Approach and the Kalai-Smorodinsky Solution

Abstract

Abstract. The purpose of this work is to present a model for portfolio multi-optimization, in which distributions are compared on the basis of tow statistics: the expected value and the Conditional Value-at-Risk (CVaR), to solve such a problem many authors have developed several algorithms, in this work we propose to find the efficient boundary by using the Normal Boundary Intersection approach (NBI) based on our proposed hybrid method SASP, since the considered problem is multi-objective, then we find the Kalai-smorodinsky solution.

Systematic Initialization Approaches for Portfolio Optimization Problems

“…For each parameter set, the algorithm requires a numerical icon (for example in EFRRR3 for k = 10, and EFRRR5 for k = 20). In EFRRR, k ∈ [1,20] is the major parameter for balancing the convergence and diversity of the solutions −k = {1, 5, 10, 15, 20, 2}. For the KnEA algorithm, T ∈ (0, 1) is given with respect to the problems, where a smaller T helps the algorithm to escape from local Pareto fronts −T = {0.6, 0.4, 0.3, 0.5}.…”

“…For the KnEA algorithm, T ∈ (0, 1) is given with respect to the problems, where a smaller T helps the algorithm to escape from local Pareto fronts −T = {0.6, 0.4, 0.3, 0.5}. MaOEA-DDFC has two parameters L and K , which influence the information convergence and estimate the directional density, respectively; −[K , L] = { [10,3], [20,3], [5,20], [10,20], [20,20], [5,3]} −. RPEA has two additional parameters; δ ∈ (0, 1) is given for decreasing the generated reference points between maximum and minimum values of the objective function, and α ∈ (0.1, 1) is the parameter -percentage-of the individuals with the largest crowding distance that are chosen to generate reference points, −…”

“…Therefore, the border vectors remain in the next generation. Since the spread metric --is calculated by using the border points, the MOEAIGDNS provides this [10,3], MaOEADDFC2= [20,3], MaOEADDFC3= [5,20], MaOEADDFC4= [10,20], MaOEADDFC5= [20,20], MaOEADDFC6= [5,3] with Wilcoxon rank sum test W is +/ − / ≈; (+ statistically better), (− statistically worst), (≈ statistically similar). [10,3], MaOEADDFC2= [20,3], MaOEADDFC3= [5,20], MaOEADDFC4= [10,20], MaOEADDFC5= [20,20], MaOEADDFC6= [5,3] with Wilcoxon rank sum test W is +/ − / ≈; (+ statistically better), (− statistically worst), (≈ statistically similar).…”

“…The results in the paper [19] showed that the mean-variance model provides quite robust results compared to other bi-objective optimization models -conditional value-at-risk (CVaR)-. The multiobjective -bi-objective-conditional value-at-risk (CVaR) model finds the Pareto front -efficient frontier-by using a proposed hybrid method [20]. This hybrid method was proposed to find the Kalai-Smorodinsky solution which is the intersection between the Pareto front and the line passing through the utopia-point that is based on the normal boundary intersection approach (NBI) [20].…”

“…The multiobjective -bi-objective-conditional value-at-risk (CVaR) model finds the Pareto front -efficient frontier-by using a proposed hybrid method [20]. This hybrid method was proposed to find the Kalai-Smorodinsky solution which is the intersection between the Pareto front and the line passing through the utopia-point that is based on the normal boundary intersection approach (NBI) [20]. For the same cardinality constrained mean-variance model, a hybridized artificial bee colony algorithm with the operator inspired by genetic algorithms (GI-ABC) was proposed in [21].…”