We consider the problem of maximizing expected power util- ity from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the paper Shreve and Soner  (1994) . Similarly  to Kallsen and Muhle-Karbe  (2010)  , 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 . In doing so we explore and exploit the strong relationship between the shadow price and the Hamilton-Jacobi-Bellman-equation .
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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util- ity
utility
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the paper
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Ann. Appl. Probab. 4
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. Similarly
609-692
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. Similar
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Ann. Appl. Probab. 20
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1341-1358
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. In doing so we explore and exploit the strong relationship between the shadow price and the Hamilton-Jacobi-Bellman-equation