🤖 AI Summary
This study addresses the challenge of optimizing time-varying weight sequences in Double Linear Policy (DLP) by formulating it as a receding-horizon stochastic optimal control problem. The approach dynamically maximizes risk-adjusted returns subject to survivability and expected positive return constraints. A key contribution is the first derivation of an analytical gradient for this non-convex objective, which is embedded within a stochastic model predictive control (SMPC) framework and solved via the L-BFGS-B algorithm to enable closed-loop, dynamic optimization of DLP weights. Empirical results demonstrate that the proposed method significantly outperforms both fixed-weight and predetermined time-varying strategies in terms of risk-adjusted returns and drawdown control.
📝 Abstract
The Double Linear Policy (DLP) framework guarantees a Robust Positive Expectation (RPE) under optimized constant-weight designs or admissible prespecified time-varying policies. However, the sequential optimization of these time-varying weights remains an open challenge. To address this gap, we propose a Stochastic Model Predictive Control (SMPC) framework. We formulate weight selection as a receding-horizon optimal control problem that explicitly maximizes risk-adjusted returns while enforcing survivability and predicted positive expectation constraints. Notably, an analytical gradient is derived for the non-convex objective function, enabling efficient optimization via the L-BFGS-B algorithm. Empirical results demonstrate that this dynamic, closed-loop approach improves risk-adjusted performance and drawdown control relative to constant-weight and prescribed time-varying DLP baselines.