Pathwise Dynamic Programming

• 成果类型: Article
• 署名作者: Bender, Christian; Gartner, Christian; Schweizerb, Nikolaus
• 署名单位: Saarland University; Tilburg University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2017.0891
• 发表日期: 2018
• 页码: 965-995
• 关键词: Bounds; valuation; algorithm; EQUATIONS; Duality; options

摘要

We present a novel method for deriving tight Monte Carlo confidence intervals for solutions of stochastic dynamic programming equations. Taking some approximate solution to the equation as an input, we construct pathwise recursions with a known bias. Suitably coupling the recursions for lower and upper bounds ensures that the method is applicable even when the dynamic program does not satisfy a comparison principle. We apply our method to three nonlinear option pricing problems, pricing under bilateral counterparty risk, under uncertain volatility, and under negotiated collateralization.