Dynamic Weight Optimization for Double Linear Policy: A Stochastic Model Predictive Control Approach
This work addresses a specific open problem in sequential optimization for financial or control systems, representing an incremental advancement.
The paper tackled the challenge of optimizing time-varying weights in the Double Linear Policy framework by proposing a Stochastic Model Predictive Control approach, resulting in improved risk-adjusted performance and drawdown control compared to baselines.
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.