How Optimal Investment Changes with Power Utility Risk Aversion

Summary

This study examines optimal consumption and investment under power utility as relative risk aversion approaches two limiting cases: infinity and one. It establishes convergence results for optimal consumption in general semimartingale models, and for optimal trading strategies in continuous models. The limiting behaviors connect power-utility decisions with exponential and logarithmic utility.

To derive these results, the authors combine optimal-control methods, convex analysis, and backward stochastic differential equations. The document presents theoretical asymptotic results rather than a specific trading rule or empirical evaluation. Its conclusions are scoped by the model conditions: trading-strategy convergence is stated for continuous models, while the consumption result covers the broader semimartingale setting.

Key ideas

• The paper studies optimal consumption and investment as relative risk aversion approaches infinity or one.
• Optimal consumption convergence is established for general semimartingale models.
• Optimal trading-strategy convergence is established for continuous models.
• The limiting cases relate power utility to exponential and logarithmic utility.
• The analysis combines optimal control, convex analysis, and backward stochastic differential equations.

Tags

# Risk Aversion Asymptotics for Power Utility Maximization


# Risk Aversion Asymptotics for Power Utility Maximization









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).

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