Power Utility Maximization in Constrained Exponential Lévy Models

Abstract

We study power utility maximization for exponential Lévy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the Lévy 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.

22 pages; forthcoming in 'Mathematical Finance'

References in corpus (2)

• Minimal $f^q$-martingale measures for exponential Lévy processes
• The Opportunity Process for Optimal Consumption and Investment with Power Utility

Cited by in corpus (3)

• Simple Explicit Formula for Near-Optimal Stochastic Lifestyling
• Mind the Cap! -- Constrained Portfolio Optimisation in Heston's Stochastic Volatility Model
• Dynamically optimal portfolios for monotone mean--variance preferences