Shadow price of information in discrete time stochastic optimization

• 成果类型: Article
• 署名作者: Pennanen, Teemu; Perkkioe, Ari-Pekka
• 署名单位: University of London; King's College London; Technical University of Berlin
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1163-2
• 发表日期: 2018
• 页码: 347-367
• 关键词: convex functionals; Optimal investment; INTEGRALS; Recourse; Duality

摘要

The shadow price of information has played a central role in stochastic optimization ever since its introduction by Rockafellar and Wets in the mid-seventies. This article studies the concept in an extended formulation of the problem and gives relaxed sufficient conditions for its existence. We allow for general adapted decision strategies, which enables one to establish the existence of solutions and the absence of a duality gap e.g. in various problems of financial mathematics where the usual boundedness assumptions fail. As applications, we calculate conjugates and subdifferentials of integral functionals and conditional expectations of normal integrands. We also give a dual form of the general dynamic programming recursion that characterizes shadow prices of information.