Horizon dependence of utility optimizers in incomplete models

The utility maximization of terminal wealth in continuous time has a long history. Literally hundreds of papers have studied many facets of such questions. Despite of the vast amount of literature, one aspect seems not well understood to date. That is the stability of the optimizers. To the best of my knowledge, only a few papers have been published on this topic, such as [3] and [21]. This document contains a paper that I participated in during my PhD research at Carnegie Mellon University. In this paper we studied the stability problem in time horizon of utility maximization in incomplete models. The question we were interested in was how the planning horizon affected the optimal investment decision. A shorter version of this thesis has been accepted for publication (jointly with my advisor Kasper Larsen) in Finance & Stochastics. The main contribution of this work is that we identified the models that fail to be stable and we also provided conditions preventing the existence of this phenomenon.