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.
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Herczegh et al. (2015) studied this question.
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