Existence of q-Bass martingales in the semidiscrete setting

Battle Count: 81

The paper is theoretically relevant to quantitative finance through its connection to the Bass local volatility model and martingale optimal transport calibration. The semidiscrete setting directly models scenario-based marginals (e.g., policy decisions with finite outcomes). However, the paper is purely theoretical with no algorithms, implementations, or empirical results. Practical relevance comes through the cited computational works [2], [8], [9] that build on this theoretical foundation. The martingale constraint is fundamental in risk-neutral pricing and calibration.

This is a pure mathematics paper with no code or implementation. The theoretical framework involves advanced concepts from optimal transport, convex analysis, and probability theory. The geometric proof technique (convex polygonal chains, L-approximations, induction on index sets, adjugate minor analysis) is highly abstract. Any computational implementation would require significant expertise in martingale optimal transport and numerical analysis of fixed-point problems.

Pure mathematics paper with complete, self-contained proofs. All definitions, theorems, propositions, and lemmas are stated rigorously with full proofs provided in the main text and appendices. No computational experiments or data are involved. The geometric arguments and induction proofs are fully detailed.