We show that, for a utility function U: R to R having reasonable asymptotic elasticity, the optimal investment process H. S is a super-martingale under each equivalent martingale measure Q, such that E[V(dQ/dP)] < "unendlich", where V is conjugate to U. Similar results for the special case of the exponential utility were recently obtained by Delbaen, Grandits, Rheinländer, Samperi, Schweizer, Stricker as well as Kabanov, Stricker. This result gives rise to a rather delicate analysis of the "good definition" of "allowed" trading strategies H for the financial market S. One offspring of these considerations leads to the subsequent - at first glance paradoxical - example. There is a financial market consisting of a deterministic bond and two risky financial assets (S_t^1, S_t^2)_0<=t<=T such that, for an agent whose preferences are modeled by expected exponential utility at time T, it is optimal to constantly hold one unit of asset S^1. However, if we pass to the market consisting only of the bond and the first risky asset S^1, and leaving the information structure unchanged, this trading strategy is not optimal any more: in this smaller market it is optimal to invest the initial endowment into the bond. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Following [10] we continue the study of the problem of expected utility maximization in incomplete markets. Our goal is to find minimal conditions on a model and a utility function for the validity of several key assertions of the theory to hold true. In [10] we proved that a minimal condition on the utility function alone, i.e. a minimal market independent condition, is that the asymptotic elasticity of the utility function is strictly less than 1. In this paper we show that a necessary and sufficient condition on both, the utility function and the model, is that the value function of the dual problem is finite. (authors' abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"