Risk management in portfolio applications of non-convex stochastic programming

In this paper, we investigate a method to hedge nonconvex stochastic programming with CVaR constraints and apply the sample average approximation (SAA) method based on bundle method to solve it. Under some moderate conditions, the SAA solution converges to its true counterpart with probability approaching one. This technique is suitable for using by investment companies, brokerage firms, mutual funds, and any business that evaluates risks. It can be combined with analytical or scenario-based methods to optimize portfolios in which case the calculations often come down to non-convex programming. Finally, we illustrate our method by considering several portfolios in the Chinese stocks market.