Ying Hu, Peter Imkeller, Matthias Muller
Published 2005-08-24Version 1
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.
Comments: Published at http://dx.doi.org/10.1214/105051605000000188 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Applied Probability 2005, Vol. 15, No. 3, 1691-1712
On utility maximization in discrete-time financial market models
On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets
On the dual problem of utility maximization in incomplete markets
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