Optimal Consumption from Investment and Random Endowment in Incomplete Semimartingale Markets
Science Direct Working Paper No S1574-0358(04)70687-5
29 Pages Posted: 2 Apr 2018
Date Written: October 2001
Abstract
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 to its topological bidual , a space of finitely-additive measures. As an application, we treat the case of a constrained Itô-process market-model, and prove that the optimal dual processes in this case are local martingales.
Keywords: Primary, secondary, utility maximization, random endowment, incomplete markets, convex duality, stochastic processes, finitely-additive measures
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