Utility maximization in incomplete markets with random endowment

Hui Wang (**), (), Jaksa Cvitanic () and Walter Schachermayer (*), ()
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Hui Wang (**),: Department of Statistics, Columbia University, New York, NY 10027, USA Manuscript
Walter Schachermayer (*),: Department of Statistics, Probability Theory and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria

Finance and Stochastics, 2001, vol. 5, issue 2, 259-272

Abstract: This paper solves the following problem of mathematical finance: to find a solution to the problem of maximizing utility from terminal wealth of an agent with a random endowment process, in the general, semimartingale model for incomplete markets, and to characterize it via the associated dual problem. We show that this is possible if the dual problem and its domain are carefully defined. More precisely, we show that the optimal terminal wealth is equal to the inverse of marginal utility evaluated at the solution to the dual problem, which is in the form of the regular part of an element of $({\bf L}^\infty)^*$ (the dual space of ${\bf L}^\infty$).

Keywords: Utility maximization; incomplete markets; random endowment; duality (search for similar items in EconPapers)
JEL-codes: C61 G11 G12 (search for similar items in EconPapers)
Date: 2001-04-10
Note: received: November 1999; final version received: February 2000
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Citations: View citations in EconPapers (81)

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