BFS 2002 |
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Contributed Talk |
Gordan Zitkovic, Ioannis Karatzas
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 $L^1$ to its topological bidual $(L^{\infty})^*$, a space of
finitely-additive measures. As an application, we treat the case of a constrained It\^ o-process market-model.
http://www.stat.columbia.edu/~gordanz/KarZit01a.pdf