In the context of a general multivariate financial market with transaction costs, we consider the problem of maximizing expected utility from terminal wealth. In contrast with the existing literature, where only the liquidation value of the terminal portfolio is relevant, we consider general utility functions which are only required to be consistent with the structure of the transaction costs. An important feature of our analysis is that the utility function is not required to be $C^1$. Such nonsmoothness is suggested by major natural examples. Our main result is an extension of the well-known dual formulation of the utility maximization problem to this context.
"Dual Formulation of the Utility Maximization Problem Under Transaction Costs." Ann. Appl. Probab. 11 (4) 1353 - 1383, November 2001. https://doi.org/10.1214/aoap/1015345406