Risk Aversion Asymptotics for Power Utility Maximization

Abstract

We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for general semimartingale models while the convergence of the optimal trading strategy is obtained for continuous models. The limits are related to exponential and logarithmic utility. To derive these results, we combine approaches from optimal control, convex analysis and backward stochastic differential equations (BSDEs).

45 pages

References in corpus (2)

• Bounded solutions to backward SDE's with jumps for utility optimization and indifference hedging
• The Opportunity Process for Optimal Consumption and Investment with Power Utility

Cited by in corpus (7)

• The Opportunity Process for Optimal Consumption and Investment with Power Utility
• The Bellman equation for power utility maximization with semimartingales
• BSDEs in Utility Maximization with BMO Market Price of Risk
• The Limits of Leverage
• Utility based pricing and hedging of jump diffusion processes with a view to applications
• Stability of exponential utility maximization with respect to market perturbations
• Stability of the exponential utility maximization problem with respect to preferences