# Advanced Methods in Mathematical Finance

1-4 September 2015
Angers - France
Europe/Paris timezone

## On the dual problem of utility maximization in incomplete markets

2 Sep 2015, 14:50
40m
Angers - France

### Speaker

Dr Yiqing LIN (University of Vienna)

### Description

We study the dual problem of the expected utility maximization in incomplete markets with bounded random endowment. We start with the duality results of [Cvitanic-Schachermayer-Wang, 2001], in which the optimal strategy is obtained by first formulating and solving a dual problem. We observe that: in the Brownian framework, the countably additive part $Q^r$ of the dual optimizer $Q\in (L^\infty)^*$ in the settings of [Cvitanic-Schachermayer-Wang, 2001] can be represented by the terminal value of a supermartingale deflator $Y$ defined in [Kramkov-Schachermayer, 1999], which moreover is a local martingale.

### Primary author

Dr Yiqing LIN (University of Vienna)

### Co-authors

Mr Junjian YANG (University of Vienna) Mrs Lingqi Gu (University of Vienna)

 Slides