An infinite-dimensional LP duality theorem

• 成果类型: Article
• 署名作者: Clark, SA
• 署名单位: University of Kentucky
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.28.2.233.14479
• 发表日期: 2003
• 页码: 233-245
• 关键词: CONTINGENT CLAIMS; fundamental theorem; arbitrage; martingales; MARKETS; price

摘要

This paper constructs an infinite-dimensional version of the Duality Theorem for a Linear Program (LP). The algebraic dual LP is replaced with a new program called the topological dual LP that closes the range of the adjoint operator. Under some mild nondegeneracy conditions involving strict positivity, the new Duality Theorem asserts that the optimal value of the primal LP equals the optimal value of the topological dual LP. Some applications to mathematical finance are also included.