ON CONVERGENCE OF THE MAYER PROBLEMS ARISING IN THE THEORY OF FINANCIAL MARKETS WITH TRANSACTION COST

Battle Count: 108

The paper provides important theoretical foundations for portfolio optimization under transaction costs in multi-asset markets. The stability/convergence results are relevant for model calibration and robustness analysis in quantitative trading. However, the paper is purely theoretical with no practical algorithms, numerical methods, or empirical validation. It informs the theoretical understanding of when optimal strategies converge under model perturbations, which is relevant for practitioners dealing with model uncertainty, but does not directly provide implementable trading strategies.

This is a highly abstract theoretical mathematics paper. There is no implementation to perform. The results require deep expertise in stochastic analysis, convex analysis, set-valued analysis, Skorokhod topology, and mathematical finance to understand and verify. The proofs involve sophisticated techniques including Meyer-Zheng topology, Skorokhod representation theorem, Doob's theorem, Fubini's theorem, and contiguity of measures.

This is a purely theoretical mathematics paper with no code, no numerical experiments, and no datasets. Reproducibility is limited to verifying the mathematical proofs. The paper provides complete proofs of all theorems and lemmas, making the theoretical results verifiable by experts in the field.