Power Utility Maximization in Constrained Exponential L\'evy Models

We study power utility maximization for exponential L\'evy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the L\'evy triplet is constructed under minimal assumptions by solving the Bellman equation. We use a novel transformation of the model to avoid technical conditions. The consequences for q-optimal martingale measures are discussed as well as extensions to non-convex constraints.Comment: 22 pages; forthcoming in 'Mathematical Finance

On q-optimal martingale measures in exponential Lévy models

Stochastic duality, q-optimal martingale measure, Minimal entropy martingale measure, Lévy processes, 91B28, 60H10, 60G51, 60J75, G11, C61,