Scenario Tree Generation and Multi-Asset Financial Optimization Problems

We compare two popular scenario tree generation methods in the context of financial optimization: Moment matching and scenario reduction. Using a simple problem with a known analytic solution, moment matching - when ensuring absence of arbitrage - replicates this solution precisely. On the other hand, even if the scenario trees generated by scenario reduction are arbitrage-free, the solutions are biased and highly variable. These results hold for correlated and uncorrelated asset returns, as well as for normal and non-normal returns.