CRRA Investment Optimization with Dynamic Risk Constraints

Summary

This paper formulates optimal investment for an investor with constant relative risk aversion preferences in a continuous-time, incomplete market. Asset prices follow Itô processes, and trading strategies must satisfy dynamic risk constraints that vary with time and market state. The constraints are generated by risk measures, so the optimization accounts for risk limits as conditions that evolve alongside the portfolio rather than as a single fixed bound.

The authors characterize optimal strategies using a quadratic backward stochastic differential equation. For time-consistent distortion risk measures, they establish a three-fund separation result, giving a structured way to understand portfolio choice under these constraints. Numerical results illustrate how imposing risk constraints changes trading decisions. The abstract does not specify the exact risk measures, market parameters, or numerical scenarios, so it provides a theoretical framework and qualitative evidence rather than a directly reproducible trading rule or broadly quantified performance claim.

Key ideas

• The investment objective uses constant relative risk aversion preferences in an incomplete continuous-time market.
• Time- and state-dependent risk measures generate dynamic constraints on trading strategies.
• Optimal strategies are characterized through a quadratic backward stochastic differential equation.
• Time-consistent distortion risk measures yield a three-fund separation result.
• Numerical results indicate that risk constraints affect optimal trading, though the abstract omits scenario details.

Tags

# CRRA Utility Maximization under Risk Constraints


# CRRA Utility Maximization under Risk Constraints









This paper studies the problem of optimal investment with CRRA (constant, relative risk aversion) preferences, subject to dynamic risk constraints on trading strategies. The market model considered is continuous in time and incomplete. the prices of financial assets are modeled by Itô processes. The dynamic risk constraints, which are time and state dependent, are generated by risk measures. Optimal trading strategies are characterized by a quadratic BSDE. Within the class of \textit{time consistent distortion risk measures}, a three-fund separation result is established. Numerical results emphasize the effects of imposing risk constraints on trading.

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