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This paper discusses a simulation-based method for solving discrete-time multiperiod portfolio choice problems under AR(1) process. The method is applicable even if the distributions of return processes are unknown. We first generate simulation sample paths of the random returns by using AR bootstrap. Then, for each sample path and each investment time, we obtain an optimal portfolio estimator, which optimizes a constant relative risk aversion (CRRA) utility function. When an investor considers an optimal investment strategy with portfolio rebalancing, it is convenient to introduce a value function. The most important difference between single-period portfolio choice problems and multiperiod ones is that the value function is time dependent. Our method takes care of the time dependency by using bootstrapped sample paths. Numerical studies are provided to examine the validity of our method. The result shows the necessity to take care of the time dependency of the value function.

We study the estimation of optimal portfolios for a Reserve Fund with an end-of-period target and when the returns of the assets that constitute the Reserve Fund portfolio follow two specifications. In the first one, assets are split into short memory (bonds) and long memory (equity), and the optimality of the portfolio is based on maximizing the Sharpe ratio. In the second, returns follow a conditional heteroskedasticity autoregressive nonlinear model, and we study when the distribution of the innovation vector is heavy-tailed stable. For this specification, we consider appropriate estimation methods, which include bootstrap and empirical likelihood.