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To any utility maximization problem under transaction costs one can assign a frictionless model with a price process S ∗, lying in the bid/ask price interval \([\underline{S}, \overline{S}]\). Such a process S ∗ is called a shadow price if it provides the same optimal utility value as in the original model with bid-ask spread.

On the game interpretation of a shadow price process in utility maximization problems under transaction costs