Convex Duality in Stochastic Optimization and Mathematical Finance

• 成果类型: Article
• 署名作者: Pennanen, Teemu
• 署名单位: University of Jyvaskyla
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1110.0485
• 发表日期: 2011
• 页码: 340-362
• 关键词: fundamental theorem; Optimal investment; transaction costs; INTEGRALS; consumption; multipliers; martingales; arbitrage

摘要

This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension of some useful techniques from these two fields to a much wider class of problems. In particular, combining certain finite-dimensional techniques from convex analysis with measure theoretic techniques from mathematical finance, we are able to close the duality gap in some situations where traditional topological arguments fail.