TRADING WITH SMALL NONLINEAR PRICE IMPACT

• 成果类型: Article
• 署名作者: Caye, Thomas; Herdegen, Martin; Muhle-Karbe, Johannes
• 署名单位: Dublin City University; University of Warwick; Imperial College London
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1513
• 发表日期: 2020
• 页码: 706-746
• 关键词: entropy martingale measure; asymptotic analysis; Utility maximization; sensitivity-analysis; Optimal investment; OPTIMAL PORTFOLIO; optimal tracking; MARKETS; MODEL; Discretization

摘要

We study portfolio choice with small nonlinear price impact on general market dynamics. Using probabilistic techniques and convex duality, we show that the asymptotic optimum can be described explicitly up to the solution of a nonlinear ODE, which identifies the optimal trading speed and the performance loss due to the trading friction. Previous asymptotic results for proportional and quadratic trading costs are obtained as limiting cases. As an illustration, we discuss how nonlinear trading costs affect the pricing and hedging of derivative securities and active portfolio management.