Comparison principle approach to utility maximization
Volume 105 / 2015
Banach Center Publications 105 (2015), 143-158
MSC: Primary 60H07, 91G10; secondary 60G44, 60H07, 60H15, 93E03, 93E20.
DOI: 10.4064/bc105-0-10
Abstract
We consider the problem of optimal investment for maximal expected utility in an incomplete market with trading strategies subject to closed constraints. Under the assumption that the underlying utility function has constant sign, we employ the comparison principle for BSDEs to construct a family of supermartingales leading to a necessary and sufficient condition for optimality. As a consequence, the value function is characterized as the initial value of a BSDE with Lipschitz growth.
