Fixed Points for the q-Bass Martingale: Existence, Stability, and Convergence

Battle Count: 107

The paper is primarily foundational mathematics in optimal transport and probability theory. Its relevance to quantitative trading is indirect: (1) the Bass Local Volatility model calibration is directly relevant to derivatives pricing and hedging; (2) martingale optimal transport has applications in model-free finance and robust pricing; (3) the dynamic reinsurance application mentioned in Remark 7.8 connects to insurance mathematics. However, the paper does not propose trading strategies, forecasting models, or directly applicable quantitative finance tools. It provides theoretical guarantees for a construction used in financial mathematics.

The paper is entirely theoretical with no implementation provided. The mathematical machinery involves: infinite-dimensional Fréchet calculus, generalized Helly selection theorems, martingale representation theorems for additive processes with jumps, adapted Wasserstein distances on Skorokhod space, and convex analysis of integrated quantile functions. Implementing the fixed-point iteration algorithm (Section 6) would require careful handling of quantile functions, monotone transport maps, and convergence criteria. The dynamic formulation (Section 7) requires stochastic calculus with semimartingale decompositions.

As a pure mathematics paper, all results are established through rigorous proofs. The theoretical framework is fully self-contained with precise definitions, assumptions, and theorem statements. No computational experiments are needed for verification. The fixed-point iteration algorithm described in Section 6 could be implemented numerically, but no code is provided.