Before revision: This paper studies a non-concave optimization problem under a Value-at-Risk (VaR) or an Expected Shortfall (ES) constraint . The non-concavity of the problem stems from the non-linear payoff structure of the optimizing investor .
After revision: This paper studies a non-concave optimization problem under a Value-at-Risk (VaR) or an Expected Shortfall (ES) constraint corresponding to a non-concave optimization problem under constraints .