CONTINUOUS-TIME DUALITY FOR SUPERREPLICATION WITH TRANSIENT PRICE IMPACT

• 成果类型: Article
• 署名作者: Bank, Peter; Dolinsky, Yan
• 署名单位: Technical University of Berlin; Hebrew University of Jerusalem; Monash University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1498
• 发表日期: 2019
• 页码: 3893-3917
• 关键词: super-replication theorem; Portfolio optimization; Optimal investment; transaction costs; optimal execution; shadow prices; free-boundary; MARKETS; manipulation; consumption

摘要

We establish a superreplication duality in a continuous-time financial model as in (Bank and Vo beta (2018)) where an investor's trades adversely affect bid- and ask-prices for a risky asset and where market resilience drives the resulting spread back towards zero at an exponential rate Similar to the literature on models with a constant spread (cf., e.g., Math. Finance 6 (1996) 133-165; Ann. Appl. Probab. 20 (2010) 1341-1358; Ann. Appl. Probab. 27 (2017) 1414-1451), our dual description of superreplication prices involves the construction of suitable absolutely continuous measures with martingales close to the unaffected reference price. A novel feature in our duality is a liquidity weighted L- (2)-norm that enters as a measurement of this closeness and that accounts for strategy dependent spreads. As applications, we establish optimality of buy-and-hold strategies for the superreplication of call options and we prove a verification theorem for utility maximizing investment strategies.