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.
Publié le : 2004-05-14
Classification:
Utility maximization,
random endowment,
convex duality,
incomplete markets,
optimal investment,
utility-based valuation,
contingent claim,
European option,
90A09,
90A10,
90C26
@article{1082737114,
author = {Hugonnier, Julien and Kramkov, Dmitry},
title = {Optimal investment with random endowments in incomplete markets},
journal = {Ann. Appl. Probab.},
volume = {14},
number = {1},
year = {2004},
pages = { 845-864},
language = {en},
url = {http://dml.mathdoc.fr/item/1082737114}
}
Hugonnier, Julien; Kramkov, Dmitry. Optimal investment with random endowments in incomplete markets. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp. 845-864. http://gdmltest.u-ga.fr/item/1082737114/