Consumption-Investment Problem in Rank-Based Models

Battle Count: 194

Highly relevant to quantitative trading and portfolio management. The paper provides explicit optimal portfolio allocation rules in rank-based models, which capture realistic market features (capital distribution stability). The open market constraint framework directly applies to index-based investing (e.g., S&P 500). The Merton-type solution structure provides actionable trading rules. However, it is primarily theoretical without empirical validation or backtesting.

The mathematical framework is complex, involving reflected SDEs, HJB equations with Neumann boundary conditions, and verification theorems. However, the final explicit solutions for first-order models are relatively straightforward to implement: compute the Merton fraction using ranked drift and covariance, then map back to named assets via rank identification. The main implementation challenge is the rank identification and the collision estimator for drift calibration.

The paper is fully theoretical with complete proofs and explicit formulas. All mathematical derivations are self-contained. However, there is no numerical implementation or code provided. The results are verifiable through the mathematical proofs presented. The first-order model solutions are fully explicit and can be independently verified.