TY - GEN A1 - Hu, Ying A1 - Imkeller, Peter A1 - Müller, Matthias T1 - Utility maximization in incomplete markets N2 - We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors’ trading strategies we allow underly constraints described by closed, but not necessarily convex, sets. The final wealths obtained by trading under these constraints are identified as stochastic processes which usually are supermartingales, and even martingales for particular strategies. These strategies are seen to be optimal, and the corresponding value functions determined simply by the initial values of the supermartingales. We separately treat the cases of exponential, power and logarithmic utility. Y1 - 2004 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/44 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-444 ER -