Published April 2001
| public
Journal Article
Utility maximization in incomplete markets with random endowment
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 (L^∞)∗ (the dual space of L^∞).
Additional Information
© 2001 Springer-Verlag Berlin Heidelberg. Manuscript received: November 1999; final version received: February 2000. Research supported in part by the NSF Grant DMS-97-32810. Support by the Austrian Science Foundation (FWF) under grant SFB#010 and by the Austrian National Bank under grant 'Jubilaumsfondprojekt Number 7049' is greatfully acknowledged.Additional details
- Eprint ID
- 78202
- Resolver ID
- CaltechAUTHORS:20170614-102418542
- DMS-97-32810
- NSF
- SFB#010
- Fonds zur Förderung der wissenschaftlichen Forschung
- 7049
- Austrian National Bank
- Created
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2017-06-14Created from EPrint's datestamp field
- Updated
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2023-06-01Created from EPrint's last_modified field