Optimal investment with random endowments in incomplete markets

Details Optimal investment with random endowments in incomplete markets Optimal investment with random endowments in incomplete markets

2004-05-14

arxiv.org/abs/math/0405293v1

Annals of Applied Probability 2004, Vol. 14, No. 2, 845-864

Mathematics

Probability

Scientific paper

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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