Scenario Tree Generation by Clustering the Simulated Data Paths

Multistage stochastic programs are effective for solving long-term planning problems under uncertainty. Such programs are usually based on a scenario model of future environment developments. A good approximation of the underlying stochastic process may involve a very large number of scenarios and their probabilities. We discuss the case when enough data paths can be generated, but due to solvability of stochastic program the scenario tree has to be constructed. The proposed strategy is to generate the multistage scenario tree from the set of individual scenarios by bundling scenarios based on cluster analysis. The K-means clustering approach is modified to capture the interstage dependencies in order to model the sequential decisions. The described scenario tree generation method is implemented on sampled data of nominal interest rate.