Algorithms for handling CVaR-constraints in dynamic stochastic programming models with applications to finance

Abstract

We propose dual decomposition and solution schemes for multistage CVaR-constrained problems. These schemes meet the need for handling multiple CVaR-constraints for different time frames and at different confidence levels. Hence they allow shaping distributions according to the decision maker's preference.With minor modifications, the proposed schemes can be used to decompose further types of risk constraints in dynamic portfolio management problems. We consider integrated chance constraints, second-order stochastic dominance constraints, and constraints involving a special value-of-information risk measure. We also suggest application to further financial problems. We propose a dynamic risk-constrained optimization model for option pricing. Moreover we propose special mid-term constraints for use in asset-liability management.