Stochastic Optimal Control of Hawkes Jump-Diffusion Systems

Battle Count: 81

The paper has indirect relevance to quantitative trading. While it does not address trading strategies, portfolio construction, or market microstructure directly, its framework for modeling rare catastrophic events with self-excitation (clustering of disasters) is relevant to tail-risk modeling, disaster risk pricing, and regime-switching strategies. The Hawkes process modeling of event clustering could inform volatility modeling and jump-risk assessment. However, the paper is firmly in the domain of mathematical economics and stochastic control theory rather than financial engineering or trading.

This is a highly advanced pure mathematics paper requiring deep expertise in stochastic analysis, point process theory, jump-diffusion SDEs, HJB equations, and stochastic optimal control. The proofs involve Poisson embedding, localization arguments, Itô formulas for jump semimartingales, Burkholder-Davis-Gundy inequalities, Gronwall's inequality, compensation formulas, and verification arguments. There is no computational implementation described. The mathematical machinery is at the frontier of stochastic control theory for jump processes.

This is a purely theoretical mathematics paper with no computational experiments, code, or empirical data. Reproducibility is limited to verifying the mathematical proofs and derivations. All results are analytical (theorems, propositions, lemmas with proofs). No numerical simulations or code repositories are provided.