Robust algorithmic trading in a generalized lattice market

Abstract

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