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May 2004 Optimal investment with random endowments in incomplete markets
Julien Hugonnier, Dmitry Kramkov
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Ann. Appl. Probab. 14(2): 845-864 (May 2004). DOI: 10.1214/105051604000000134


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.


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Julien Hugonnier. Dmitry Kramkov. "Optimal investment with random endowments in incomplete markets." Ann. Appl. Probab. 14 (2) 845 - 864, May 2004.


Published: May 2004
First available in Project Euclid: 23 April 2004

zbMATH: 1086.91030
MathSciNet: MR2052905
Digital Object Identifier: 10.1214/105051604000000134

Primary: 90A09 , 90A10 , 90C26

Keywords: Contingent claim , convex duality , European option , incomplete markets , optimal investment , random endowment , utility maximization , utility-based valuation

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.14 • No. 2 • May 2004
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