Stochastic Control Problems with Infinite Horizon and Regime Switching Arising in Optimal Liquidation with Semimartingale Strategies

Battle Count: 83

Highly relevant to quantitative trading, particularly optimal execution and liquidation strategies. The paper provides rigorous mathematical foundations for infinite-horizon liquidation with regime switching, which is directly applicable to algorithmic trading systems that must adapt to changing market regimes. The semimartingale strategy framework allows for realistic modeling of trading strategies. However, the purely theoretical nature means direct implementation requires significant additional work.

Extremely high complexity. The paper involves advanced stochastic analysis including BMO martingale theory, reverse Hölder inequalities, comparison theorems for multi-dimensional BSDEs, Itô's formula for regime-switching processes, and Doléans-Dade stochastic exponentials. Any numerical implementation would require solving coupled systems of infinite-horizon BSDEs with unbounded stochastic coefficients, which is computationally very challenging.

This is a purely theoretical mathematics paper with no computational experiments, code, or empirical data. Reproducibility would require independently verifying all proofs and theorems. No numerical implementations or simulations are provided.