AN ITERATED AZEMA-YOR TYPE EMBEDDING FOR FINITELY MANY MARGINALS

• 成果类型: Article
• 署名作者: Obloj, Jan; Spoida, Peter
• 署名单位: University of Oxford
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1110
• 发表日期: 2017
• 页码: 2210-2247
• 关键词: barrier options; maximum maximum; brownian-motion; CONSTRUCTION; martingales

摘要

We solve the n-marginal Skorokhod embedding problem for a continuous local martingale and a sequence of probability measures mu(1),...,mu(n) which are in convex order and satisfy an additional technical assumption. Our construction is explicit and is a multiple marginal generalization of the Azema and Yor [In Seminaire de Probabilites, XIII (Univ. Strasbourg, Strasbourg, 1977/78) (1979) 90-115 Springer] solution. In particular, we recover the stopping boundaries obtained by Brown, Hobson and Rogers [Probab. Theory Related Fields 119 (2001) 558-578] and Madan and Yor [Bernoulli 8 (2002) 509-536]. Our technical assumption is necessary for the explicit embedding, as demonstrated with a counterexample. We discuss extensions to the general case giving details when n = 3. In our analysis we compute the law of the maximum at each of the n stopping times. This is used in Henry-Labordere et al. [Ann. Appl. Probab. 26 (2016) 1-44] to show that the construction maximizes the distribution of the maximum among all solutions to the n-marginal Skorokhod embedding problem. The result has direct implications for robust pricing and hedging of Lookback options.