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.

Motivated by a hedging problem in mathematical nance, El Karoui and Quenez 7] and Kramkov 1 4 ] h a ve d e v eloped optional versions of the Doob-Meyer decomposition which hold simultaneously for all equivalent martingale measures. We i n vestigate the general structure of such optional decompositions, both in additive and in multiplicative form, and under constraints corresponding to di erent classes of equivalent measures. As an application, we extend results of Karatzas and Cvitani c 3] on hedging problems with constrained portfolios.

No abstract

In the general framework of a semimartingale financial model and a utility function U defined on the positive real line, we compute the first-order expansion of marginal utility-based prices with respect to a "small" number of random endowments. We show that this linear approximation has some important qualitative properties if and only if there is a risk-tolerance wealth process. In particular, they hold true in the following polar cases:

No abstract