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 [5] and prove the following statement: in the Brownian framework, the countably additive part Q r of the dual optimizer Q ∈ (L ∞ ) * obtained in [5] can be represented by the terminal value of a supermartingale deflator Y defined in [21], which is a local martingale.
In this paper, we consider a numéraire-based utility maximization problem under constant proportional transaction costs and random endowment. Assuming that the agent cannot short sell assets and is endowed with a strictly positive contingent claim, a primal optimizer of this utility maximization problem exists. Moreover, we observe that the original market with transaction costs can be replaced by a frictionless shadow market that yields the same optimality. On the other hand, we present an example to show that in some case when these constraints are relaxed, the existence of shadow prices is still warranted.
MSC2010. 91B16; 91G10
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