Geometric and Arithmetic Likelihood Aggregation for Diffusions with Heterogeneous Volatility

Battle Count: 82

Highly relevant for quantitative finance applications involving model aggregation under uncertainty. Provides rigorous theoretical foundation for combining diffusion models with different drift and volatility specifications. Directly applicable to: (1) selecting consensus pricing measures, (2) aggregating stochastic volatility models (Heston, CIR), (3) understanding how drift disagreement inflates or reduces selected volatility, (4) martingale-constrained aggregation for traded assets. The explicit formulas for OU and CIR barycenters are practically useful. However, the paper is primarily theoretical and does not provide trading strategies or backtests.

Extremely high complexity. Requires deep expertise in stochastic analysis, optimal transport theory (Bures-Wasserstein geometry), Hamilton-Jacobi-Bellman PDE theory, convex optimization on matrix spaces, and mathematical finance. Implementation would require: solving HJB equations numerically, computing Bures-Wasserstein barycenters of positive definite matrices, handling degenerate diffusions (CIR), and managing martingale constraints. The theoretical results are explicit for scalar OU and CIR cases but matrix-valued problems require sophisticated numerical methods.

Purely theoretical paper with complete mathematical proofs. All results are derivable from stated assumptions. No empirical data or code required. Figure 1 parameters are fully specified. The mathematical framework is self-contained with explicit formulas for all selectors.