PATH DEPENDENT OPTIMAL TRANSPORT AND MODEL CALIBRATION ON EXOTIC DERIVATIVES

• 成果类型: Article
• 署名作者: Guo, Ivan; Loeper, Gregoire
• 署名单位: Monash University; Monash University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1617
• 发表日期: 2021
• 页码: 1232-1263
• 关键词: viscosity solutions; benamou-brenier; duality theorem

摘要

In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the solution in terms of path dependent partial differential equations (PPDEs). Moreover, we provide a dimension reduction result based on the new notion of semifiltrations, which identifies appropriate Markovian state variables based on the constraints and the cost function. Our technique is then applied to the exact calibration of volatility models to the prices of general path dependent derivatives.