Abstract
Risk management aims to minimize the downside of decisions made in stochastic environments. Quantile is the most popular metrics used in risk management. In this paper, we present a newly-developed methodology, called Stochastic Nelder-Mead Simplex Method for Quantile Optimization (SNM-Q), that can handle quantile-based stochastic optimization problems. We also present SNM-Q based on penalty function method that can solve problems with constraints. An extensive numerical study shows that SNM-Q can efficiently and effectively solve the problem and thus is worth further investigation.