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Shadow price in the power utility case

Attila Herczegh and Vilmos Prokaj

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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.

Date: 2011-12, Revised 2015-09
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Published in Annals of Applied Probability 2015, Vol. 25, No. 5, 2671-2707

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