Shadow price in the power utility case
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.
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