# Utility maximization in incomplete markets with random endowment

## Author

Listed:
• (**), Hui Wang

(Department of Statistics, Columbia University, New York, NY 10027, USA Manuscript)

• Jaksa Cvitanic

(Department of Mathematics, USC, 1042 W 36 Pl, DRB 155, Los Angeles, CA 90089-1113, USA)

• (*), Walter Schachermayer

(Department of Statistics, Probability Theory and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria)

## 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 ${\bf L}^\infty$).

## Suggested Citation

• (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
• Handle: RePEc:spr:finsto:v:5:y:2001:i:2:p:259-272
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### Keywords

Utility maximization; incomplete markets; random endowment; duality;
All these keywords.

### JEL classification:

• G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
• G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
• C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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