Power Utility Maximization in Constrained Exponential Lévy Models

Details Power Utility Maximization in Constrained Exponential Lévy Models Power Utility Maximization in Constrained Exponential Lévy Models

2009-12-09

arxiv.org/abs/0912.1885v2

Economy

Quantitative Finance

Portfolio Management

22 pages; forthcoming in 'Mathematical Finance'

Scientific paper

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.

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