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We discuss a portfolio management problem of the rational policyholder of a variable annuity (VA) with maturity guarantee who aims to maximize the utility of her terminal wealth. We consider a VA contract which allows the policyholder to modify her investment mix throughout the contract. This problem is formulated in terms of constrained optimal stochastic controland requires the maximization of a non-concave utility function. We solve the problem using a martingale approach and compare with existing results. In particular, we show that there exist different ways to set the guarantee fee, which impacts the policyholder's optimal investment strategy and the resulting cost to the insurer.