We introduce a method that relies exclusively on Monte Carlo simulation in order to compute numerically optimal portfolio values for utility maximization problems. Our method is quite general and only requires complete markets and knowledge of the dynamics of the security processes. It can be applied regardless of the number of factors and of whether the agent derives utility from intertemporal consumption, terminal wealth or both. We also perform some comparative statics analysis. Our comparative statics show that risk aversion has by far the greatest influence on the value of the optimal portfolio
