CRRA Utility Maximization under Risk Constraints
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abstract
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 It\^o 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.