Risk-Sensitive Investment Management via Free Energy–Entropy Duality

Battle Count: 70

Highly relevant to quantitative trading and portfolio management. The paper provides explicit, implementable optimal portfolio weights in a factor-based setting with benchmarking. The fractional Kelly interpretation and the connection to RL (policy-gradient methods) make it directly applicable to systematic portfolio construction. The numerical implementation on U.S. equity ETFs demonstrates practical tractability. The equivalence proof between two solution methods adds confidence for practitioners.

The analytical solution is fully explicit: optimal controls are affine feedback maps requiring solutions to a matrix Riccati ODE, a linear ODE, and a scalar integral. Parameter estimation from factor data is standard (regression for drifts, quadratic variation for diffusion). The main complexity lies in correctly implementing the multi-dimensional Riccati equation solver and the Girsanov change of measure. The RL extension (companion paper) would add significant complexity. For the deterministic-parameter case, implementation is moderate.

The paper provides fully explicit analytical formulas for optimal controls, value function coefficients (Riccati equation, linear ODE, integral), and a clear implementation framework. However, no code repository is provided. The implementation section uses publicly available data (Kenneth French's data library) and CRSP data (subscription required). The methodology is deterministic given estimated parameters, making analytical reproduction feasible, but the numerical simulation details (5000 paths, 1260 steps) would need to be coded from scratch.