On the dual problem of utility maximization in incomplete markets

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 Cvitanić et al. (2001) and prove the following statement: in the Brownian framework, the countably additive part Q̂r of the dual optimizer Q̂∈(L∞)∗ obtained in Cvitanić et al. (2001) can be represented by the terminal value of a supermartingale deflator YY defined in Kramkov and Schachermayer (1999), which is a local martingale.