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We consider the problem of dynamic portfolio optimization in a discrete-time, finite-horizon setting. Our general model considers risk aversion, portfolio constraints (e.g., no short positions), return predictability, and transaction costs. This problem is naturally formulated as a stochastic dynamic program. Unfortunately, with nonzero transaction costs, the dimension of the state space is at least as large as the number of assets, and the problem is very difficult to solve with more than one or two assets. In this paper, we consider several easy-to-compute heuristic trading strategies that are based on optimizing simpler models. We complement these heuristics with upper bounds on the performance with an optimal trading strategy. These bounds are based on the dual approach developed in Brown et al. (Brown, D. B., J. E. Smith, P. Sun. 2009. Information relaxations and duality in stochastic dynamic programs. Oper. Res. 58(4) 785–801). In this context, these bounds are given by considering an investor who has access to perfect information about future returns but is penalized for using this advance information. These heuristic strategies and bounds can be evaluated using Monte Carlo simulation. We evaluate these heuristics and bounds in numerical experiments with a risk-free asset and 3 or 10 risky assets. In many cases, the performance of the heuristic strategy is very close to the upper bound, indicating that the heuristic strategies are very nearly optimal. This paper was accepted by Dimitris Bertsimas, optimization.
Brown et al. (Sat,) studied this question.