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>

The paper studies the robust maximization of utility from terminal wealth in a diffusion financial market model. The underlying model consists of a tradable risky asset whose price is described by a diffusion process with misspecified trend and volatility coefficients, and a non-tradable asset...

For inequality constrained optimization problem, we show the existence of local saddle point of generalized augmented Lagrangian under weak second-order sufficient conditions which are weaker than the second-order sufficient conditions in the literature. We further discuss the existence of...