Expected Utility Maximization for Competitive Agents

Portfolio optimization is one of the central topics in continuous-time mathematical finance. A relatively recent development in the field of portfolio optimization is the inclusion of competition between investors, motivated by the vast variety of empirical evidence for competition between fund managers.
This thesis is focused on portfolio optimization problems in continuous time for some (infinitely) large number of agents who base their decisions on relative performance concerns. In five main chapters, we take a look at such problems from various perspectives and on different levels of generality. The competitive feature is incorporated in three different ways – via the objective function, in a stochastic constraint, and via cumulative price impact. In each of these situations, we are able to find explicit solutions to the emerging multi-objective optimization problems applying two different notions of optimality.