A Neural Network Model on Solving Multiobjective Conditional Value-at-Risk

Conditional Value-at-Risk (CVaR) is a new approach for credit risk optimization in the field of finance engineering. This paper introduces the concept of α-CVaR for the case of multiple losses under the confidence level vector α. The problem of solving the minimal α-CVaR results in a multiobjective problem (MCVaR). In order to get Pareto efficient solutions of the (MCVaR), we introduce a single objective problem (SCVaR) and show that the optimal solutions of the (SCVaR) are Pareto efficient solutions of (MCVaR). We construct a nonlinear neural networks model with an approximate problem (SCVaR)′ of (SCVaR). We may get an approximate solution (SCVaR) by solving this nonlinear neural networks model.