A STOCHASTIC CONTROL APPROACH TO NO-ARBITRAGE BOUNDS GIVEN MARGINALS, WITH AN APPLICATION TO LOOKBACK OPTIONS

• 成果类型: Article
• 署名作者: Galichon, A.; Henry-Labordere, P.; Touzi, N.
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP925
• 发表日期: 2014
• 页码: 312-336
• 关键词: optimal transportation; Contingent claims; maximum

摘要

We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). Instead, we provide a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem. We then show that this formulation allows us to recover previously known results about lookback options. In particular, our methodology induces a new proof of the optimality of Azema-Yor solution of the SEP for a certain class of lookback options. Unlike the SEP technique, our approach applies to a large class of exotics and is suitable for numerical approximation techniques.