Minimizing Benchmark-Relative Drawdown Duration via Occupation Time Penalization

Battle Count: 98

Highly relevant for active portfolio management and benchmark-relative investing strategies. The projection-based feedback control provides a tractable framework for managing benchmark-relative drawdown duration, which is critical for institutional investors (pension funds, mutual funds, hedge funds) evaluated relative to benchmarks. However, the paper is primarily theoretical with limited practical implementation guidance. The numerical experiments demonstrate the strategy's effectiveness in reducing time spent in critical drawdown compared to buy-and-hold, but the model assumptions (continuous trading, no transaction costs, specific market structure) limit direct applicability to real-world trading systems.

High complexity due to: (1) solving the HJB ODE system via Picard-Lindelof iteration, (2) computing metric projections onto convex sets for the feedback control, (3) simulating reflected SDEs with discontinuous coefficients, (4) verifying smooth-fit and matching conditions at the drawdown threshold, (5) handling the geometric conditions for strong well-posedness. The projection-based control requires solving constrained optimization problems at each time step. Monte Carlo validation with 5000 paths adds computational burden.

The paper provides complete theoretical derivations, explicit parameter values for numerical experiments (Section 5), and detailed proofs in appendices. However, no code repository is provided. The numerical experiments use Monte Carlo simulation with 5000 paths, weekly rebalancing over 24 years, and specified parameters. Reproduction would require implementing the HJB solver, projection-based feedback control, and reflected SDE simulation from scratch.