Inverse cutting plane methods for optimization problems with second-order stochastic dominance constraints

Abstract

We propose new cutting plane methods for solving optimization problems with second-order stochastic dominance constraints. The methods are based on the inverse formulation of stochastic dominance constraints using Lorenz functions. Convergence of the methods is proved for general probability distributions. For general discrete distributions convergence is finite. Numerical experiments on a portfolio problem confirm efficiency of the methods.

Keywords:

• stochastic dominance
• cutting plane methods
• Lorenz curve
• portfolio optimization
• conditional value-at-risk

AMS Subject Classifications:

• 90C15
• 90C48
• 65K05
• 90C05
• 60E15

Acknowledgements

This research was supported by the NSF awards DMS-0603728 and DMS-0604060. The authors are grateful to two anonymous referees for constructive remarks.