To any utility maximization problem under transaction costs one can assign a frictionless model with a price process S <Superscript>∗</Superscript>, lying in the bid/ask price interval <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$[\underline{S}, \overline{S}]$</EquationSource> </InlineEquation>. Such a process S <Superscript>∗</Superscript> is called a shadow price if it provides the same optimal utility value as in the...</superscript></equationsource></inlineequation></superscript>