Optimal payoff under Bregman-Wasserstein divergence constraints
This paper studies the optimal payoff selection problem for expected utility maximizers under a Bregman–Wasserstein (BW) divergence constraint, designed to control deviation from a reference payoff while allowing asymmetric penalties for upside and downside deviations—better aligning with real-world investment objectives. Methodologically, it provides the first analytical solution to the optimal payoff structure under BW divergence constraints, employing a convex function φ to flexibly encode directional deviation preferences and thereby overcoming the symmetry limitation inherent in classical Wasserstein distance. By integrating convex analysis, optimal transport theory, and stochastic optimization, the authors formulate a utility maximization framework regularized by a Bregman penalty term. Theoretically, they derive a closed-form expression for the optimal payoff. Numerical experiments demonstrate that tuning φ enables precise calibration of risk attitudes and significantly improves alignment between payoff allocation and investor-specific goals.