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

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 preferences. With minor modifications, the proposed schemes call be used to decompose further types of risk constraints in 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 an 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.