# On the dual problem of utility maximization in incomplete markets

arXiv: https://arxiv.org/abs/1510.08323 · HTML: https://mlsanity.com/paper/1510.08323/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2015.

## Built on by (most cited first, 1 of 1)

- [Deep Learning Methods for S Shaped Utility Maximisation with a Random Reference Point](https://mlsanity.com/paper/2410.05524/) (2024)

## Abstract (arXiv)

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 Qr of the dual optimizer Q∈ (L^∞)^* 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.