Sampled-Data Wasserstein Distributionally Robust Control of Multiplicative Systems: A Convex Relaxation with Performance Guarantees

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Highly relevant to quantitative trading. The paper directly addresses log-optimal portfolio control (Kelly criterion) with transaction costs, adaptive rebalancing frequency selection, and distributional robustness. The empirical validation on S&P 500 constituents demonstrates practical applicability. The adaptive sampling scheme that dynamically adjusts rebalancing frequency based on market conditions is directly applicable to real-world portfolio management. The framework provides certified performance floors for capital growth rates, which is valuable for risk-aware trading strategies.

High implementation complexity. Requires solving convex optimization programs with semi-infinite constraints (via cutting-plane methods), Wasserstein ambiguity set calibration (via concentration bounds or block bootstrap), joint optimization over discrete sampling periods and continuous control vectors, and handling of multiplicative dynamics with viability constraints. The mathematical machinery (Fenchel conjugates, minimax inequalities, ergodic theory) is sophisticated. However, the final formulation is a standard convex program solvable with existing solvers (e.g., CVX, MOSEK).

The paper provides detailed mathematical formulations, a complete cutting-plane algorithm (Algorithm A.1), explicit parameter settings (candidate sampling periods, look-back window, transaction cost rates), and uses publicly available data (Yahoo Finance stock prices, CBOE Treasury Bill yields). However, no code repository is explicitly linked, and some implementation details (e.g., block bootstrap calibration for ambiguity radii) are described at a high level.