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Shadow price in the power utility case

Research paper by Attila Herczegh, Vilmos Prokaj

Indexed on: 09 Sep '15Published on: 09 Sep '15Published in: arXiv - Quantitative Finance - Portfolio Management



Abstract

We consider the problem of maximizing expected power utility from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in Shreve and Soner [Ann. Appl. Probab. 4 (1994) 609-692]. Similar to Kallsen and Muhle-Karbe [Ann. Appl. Probab. 20 (2010) 1341-1358], we derive a shadow price, that is, a frictionless price process with values in the bid-ask spread which leads to the same optimal policy.