Modeling and Stabilizing Financial Systemic Risk Using Optimal Control Theory

Battle Count: 63

The paper is primarily relevant to macroprudential policy, systemic risk regulation, and central bank interventions rather than quantitative trading strategies. It addresses system-level financial stability rather than asset pricing, portfolio construction, or trading signals. However, understanding systemic risk dynamics could inform tail-risk hedging strategies and crisis-period portfolio management.

Extremely high complexity. Requires expertise in: (1) PDE theory and semigroup methods in infinite-dimensional spaces, (2) Optimal control theory (Pontryagin's principle, Riccati/Hamilton-Jacobi equations), (3) Functional analysis (Sobolev spaces, contraction mapping), (4) H-infinity control theory. Practical implementation would require solving operator Riccati equations in function spaces and the nonlinear Hamilton-Jacobi equation, which are computationally intensive and not straightforward to discretize.

The paper is purely theoretical with complete mathematical proofs (equations 1-108). All derivations are self-contained and verifiable. However, there are no numerical simulations, no code, and no empirical data to reproduce. The mathematical framework can be verified by experts in PDE control theory, but practical implementation would require additional work.