On the dual problem of utility maximization in incomplete markets

Lingqi Gu, Yiqing Lin, Junjian Yang

Published 2015-10-28Version 1

In this paper, we study the dual problem of the expected utility maximization in incomplete markets with bounded random endowment. We start with the problem formulated in the paper of Cvitani\'{c}-Schachermayer-Wang (2001) and prove the following statement: in the Brownian framework, the countably additive part $Q^r$ of the dual optimizer $Q\in (L^\infty)^*$ obtained in that paper can be represented by the terminal value of a supermartingale deflator $Y$ defined in the paper of Kramkov-Schachermayer (1999), which is a local martingale.