A Hybrid Simulation/Tree Stochastic Optimization Model for Dynamic Asset Allocation

Asset allocation decisions are critical for investors with diversiaed portfolios. Institutional investors must manage their strategic asset mix over time to achieve favorable returns subject to various uncertainties, policy and legal constraints, and other requirements. In order to determine the asset mix explicitly, one may use a multi-period portfolio optimization model. The concept of scenarios is typically employed for modeling random parameters in multiperiod stochastic programming (MSP) models, and scenarios are constructed via a tree structure. Another approach for developing dynamic investment strategies, which oaers an alternative to stochastic programming, is the dynamic stochastic control. Recently, an alternative stochastic programming model with simulated paths was proposed by Hibiki (2001b, 2001c). Scenarios are constructed via a simulated path structure. The advantage of simulated paths comparing to scenario trees is higher accuracy of description of uncertainties associated with asset returns. In addition, we can make conditional decisions in this framework similarly to a scenario tree model. This model is called a hybrid model. The model is formulated as a linear programming model, which can be easily implemented and eeciently solved using sophisticated mathematical programming software. The previous papers (Hibiki 2001b, 2001c) do not have enough results to show the features of the hybrid model. In this paper, we develop the general formulation for several investment strategies, and highlight its features and properties using some numerical tests. We explain the concept, formulation and typical numerical examples of the hybrid model, the scenario generating process, and the procedure of generating extended decision tree. We present some numerical tests for various numbers of branching trees, various numbers of simulated paths, degree of the sampling error, and diaerent investment strategies. Moreover, we show the compact representation form, which is equivalent to the original form but is more eecient from computational point of view.