Robust stochastic dominance and its application to risk-averse optimization

• 成果类型: Article; Proceedings Paper
• 署名作者: Dentcheva, Darinka; Ruszczynski, Andrzej
• 署名单位: Stevens Institute of Technology; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-009-0321-6
• 发表日期: 2010
• 页码: 85-100
• 关键词: optimality conditions; expected utility; constraints; Duality

摘要

We introduce a new preference relation in the space of random variables, which we call robust stochastic dominance. We consider stochastic optimization problems where risk-aversion is expressed by a robust stochastic dominance constraint. These are composite semi-infinite optimization problems with constraints on compositions of measures of risk and utility functions. We develop necessary and sufficient conditions of optimality for such optimization problems in the convex case. In the nonconvex case, we derive necessary conditions of optimality under additional smoothness assumptions of some mappings involved in the problem.