In this paper we study the utility maximization problem on the terminal wealth with proportional transaction costs and random endowment. Under the assumption of the existence of consistent price systems, which makes the duality approach possible, we consider the duality between the primal utility maximization problem and the dual one, which is set up on the domain of finitely additive measures. In particular, we prove duality results for utility functions supporting possibly negative values. Moreover, we construct the shadow market by the dual optimal process and exhibit the utility based pricing for the random endowment.
In this paper we study the problem of maximizing expected utility from the terminal wealth with proportional transaction costs and random endowment. In the context of the existence of consistent price systems, we consider the duality between the primal utility maximization problem and the dual one, which is set up on the domain of finitely additive measures. In particular, we prove duality results for utility functions supporting possibly negative values. Moreover, we construct the shadow market by the dual optimal process and consider the utility based pricing for random endowment.
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