The Annals of Applied Probability

Optimal investment with random endowments in incomplete markets

Julien Hugonnier and Dmitry Kramkov

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Abstract

In this paper, we study the problem of expected utility maximization of an agent who, in addition to an initial capital, receives random endowments at maturity. Contrary to previous studies, we treat as the variables of the optimization problem not only the initial capital but also the number of units of the random endowments. We show that this approach leads to a dual problem, whose solution is always attained in the space of random variables. In particular, this technique does not require the use of finitely additive measures and the related assumption that the endowments are bounded.

Article information

Source
Ann. Appl. Probab., Volume 14, Number 2 (2004), 845-864.

Dates
First available in Project Euclid: 23 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1082737114

Digital Object Identifier
doi:10.1214/105051604000000134

Mathematical Reviews number (MathSciNet)
MR2052905

Zentralblatt MATH identifier
1086.91030

Subjects
Primary: 90A09 90A10 90C26: Nonconvex programming, global optimization

Keywords
Utility maximization random endowment convex duality incomplete markets optimal investment utility-based valuation contingent claim European option

Citation

Hugonnier, Julien; Kramkov, Dmitry. Optimal investment with random endowments in incomplete markets. Ann. Appl. Probab. 14 (2004), no. 2, 845--864. doi:10.1214/105051604000000134. https://projecteuclid.org/euclid.aoap/1082737114


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