On the dual problem of utility maximization in incomplete markets

Abstract

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 Cvitanić-Schachermayer-Wang (2001) and prove the following statement: in the Brownian framework, the countably additive part $Q^r$ of the dual optimizer $Q\in (L^{\infty }{)}^{\ast }$ 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.

References in corpus (3)

• Supermartingales as Radon-Nikodym densities and related measure extensions
• Strong supermartingales and limits of nonnegative martingales
• Muckenhoupt's $(A_p)$ condition and the existence of the optimal martingale measure

Cited by in corpus (3)

• Utility maximization problem under transaction costs: optimal dual processes and stability
• Consumption-investment optimization with Epstein-Zin utility in unbounded non-Markovian markets
• Utility maximization problem with random endowment and transaction costs: when wealth may become negative