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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.
Peter Imkeller, and Victor Nzengang. "Comparison principle approach to utility maximization." Banach Center Publications 105.1 (2015): 143-158. <http://eudml.org/doc/286644>.
@article{PeterImkeller2015, 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.}, author = {Peter Imkeller, Victor Nzengang}, journal = {Banach Center Publications}, keywords = {utility maximization; backward stochastic differential equations; comparison principle}, language = {eng}, number = {1}, pages = {143-158}, title = {Comparison principle approach to utility maximization}, url = {http://eudml.org/doc/286644}, volume = {105}, year = {2015}, }
TY - JOUR AU - Peter Imkeller AU - Victor Nzengang TI - Comparison principle approach to utility maximization JO - Banach Center Publications PY - 2015 VL - 105 IS - 1 SP - 143 EP - 158 AB - 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. LA - eng KW - utility maximization; backward stochastic differential equations; comparison principle UR - http://eudml.org/doc/286644 ER -