Outperforming a Benchmark with α-Bregman Wasserstein Divergence

Explore advanced portfolio management strategies in this 28-minute conference lecture that examines how investors can outperform benchmarks using α-Bregman Wasserstein divergence. Delve into the mathematical framework for active portfolio management where investors maximize expected utility of terminal wealth differences between their strategy and benchmark proportions, subject to budget and deviation constraints. Learn about the asymmetric penalization properties of α-Bregman Wasserstein divergence, which treats gains and losses differently while penalizing underperformance more heavily than outperformance. Discover how this divergence measure subsumes both Bregman Wasserstein and the widely-used Wasserstein divergence. Examine rigorous mathematical proofs establishing existence, uniqueness, and characterization of optimal portfolio strategies, along with explicit criteria determining when divergence and budget constraints become binding. Gain insights through numerical illustrations that demonstrate practical applications of these theoretical concepts in quantitative finance and optimal transport theory.