Robust Trading in a Generalized Lattice Market

This paper introduces a novel robust trading paradigm, called $\mathit{\text{multi-double}}\mathit{\text{linear}}\mathit{\text{policies}}$, situated within a $\mathit{\text{generalized}}$ lattice market. Distinctively, our framework departs from most existing robust trading strategies, which are predominantly limited to single or paired assets and typically embed asset correlation within the trading strategy itself, rather than as an inherent characteristic of the market. Our generalized lattice market model incorporates both serially correlated returns and asset correlation through a conditional probabilistic model. In the nominal case, where the parameters of the model are known, we demonstrate that the proposed policies ensure survivability and probabilistic positivity. We then derive an analytic expression for the worst-case expected gain-loss and prove sufficient conditions that the proposed policies can maintain a $\mathit{\text{positive}}\mathit{\text{expected}}\mathit{\text{profits}}$, even within a seemingly nonprofitable symmetric lattice market. When the parameters are unknown and require estimation, we show that the parameter space of the lattice model forms a convex polyhedron, and we present an efficient estimation method using a constrained least-squares method. These theoretical findings are strengthened by extensive empirical studies using data from the top 30 companies within the S&P 500 index, substantiating the efficacy of the generalized model and the robustness of the proposed policies in sustaining the positive expected profit and providing downside risk protection.