Algorithmic Aspects of Scenario-Based Multi-stage Decision Process Optimization

Multi-stage decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future uncertain values on which the decision will depend on. The quality of the scenario model severely affects the quality of the solution of the optimization model. Various approaches towards an optimal generation of discrete-state approximations (represented as scenario trees) have been suggested in the literature. Direct scenario tree sampling based on historical data or econometric models, as well as scenario path simulation and optimal tree approximation methods are discussed from an algorithmic perspective. A multi-stage financial asset management decision optimization model is presented to outline strategies to analyze the impact of various algorithmic scenario generation methodologies.