Robust Trading in a Generalized Lattice Market

TL;DR

This work addresses robust trading under model uncertainty in multi-asset markets by introducing a generalized lattice market that captures both serial correlations and asset cross-dependencies. It develops a multi-double linear policy framework that yields Robust Positive Expectation (RPE) and derives analytic bounds on worst-case gain-loss, with sufficient conditions for positive profits in trending and symmetric markets. A convex, constrained least-squares estimation approach is designed to efficiently recover the model parameters, including movement factors, correlations, and Markov coefficients. Empirical validation on the S&P 30 demonstrates the practical viability of the generalized model, the robustness of the proposed policies, and meaningful downside risk protection under realistic costs and market conditions.

Abstract

This paper introduces a novel robust trading paradigm, called \textit{multi-double linear policies}, situated within a \textit{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 \textit{positive expected 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.

Figures (10)

• Figure 1: An Illustration of Generalized Lattice Model.
• Figure 2: Example of Real Stock Prices in S&P 30 Versus Monte Carlo Simulated Sample Paths Using Generalized Lattice Model with Memory Length $m=5$.
• Figure 3: Average Cumulative Gain-Loss $\overline{\mathcal{G}}(k)$ Against Weights $\omega \in [0,1]$ for Parameter Set $(i)$ Described in Table \ref{['tab: Summary of Parameters Sets']}.
• Figure 4: Standard Deviation of Cumulative Gain-Loss ${\rm std}(\mathcal{G}(k))$ Against Weights $\omega \in [0, 1]$ for Parameter Set $(i)$ Specified in Table \ref{['tab: Summary of Parameters Sets']}.
• Figure 5: Sensitivity of $\alpha$: Average Cumulative Gain-Loss Versus Weights Under Different $\alpha$ Values.

Theorems & Definitions (27)

• Remark 2.1
• Remark 2.2
• Definition 2.1: Robust Positive Expectation
• Lemma 3.1: Probabilistic Positivity
• Remark 3.1
• Theorem 3.1: The Worst Expected Gain-Loss
• proof
• Remark 3.2: Approximate RPE
• Lemma 3.2: A Strict Convex Auxiliary Function
• Theorem 3.2: Positive Expected Profits