Optimal consumption from investment and random endowment in incomplete semimartingale markets

Karatzas, Ioannis ; Žitković, Gordan

Ann. Probab., Tome 31 (2003) no. 1, p. 1821-1858 / Harvested from Project Euclid

Résumé

We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and uniqueness result using techniques from convex duality. The notion of "asymptotic elasticity'' of Kramkov and Schachermayer is extended to the time-dependent case. By imposing no smoothness requirements on the utility function in the temporal argument, we can treat both pure consumption and combined consumption--terminal wealth problems in a common framework. To make the duality approach possible, we provide a detailed characterization of the enlarged dual domain which is reminiscent of the enlargement of $\lone$ to its topological bidual $\linfd$, a space of finitely additive measures. As an application, we treat a constrained Itô process market model, as well as a "totally incomplete'' model.

Détail

Publié le : 2003-10-14
Classification:  Utility maximization,  random endowment,  incomplete markets,  convex duality,  stochastic processes,  finitely additive measures,  91B28,  91B70,  60G07,  60G44