Infinite-Horizon Optimal Control of Jump-Diffusion Models for Pollution-Dependent Disasters

Battle Count: 84

The paper is primarily about environmental economics and stochastic control theory rather than quantitative trading. However, the mathematical tools (jump-diffusion processes, HJB equations, Poisson random measures, FBSDEs) are directly relevant to derivative pricing under jump risk, portfolio optimization with rare catastrophic events, and risk management. The pollution-dependent disaster intensity concept could be loosely analogized to state-dependent jump intensities in credit risk or commodity markets. The theoretical framework for jump-diffusion control is transferable to trading contexts but requires significant adaptation.

Extremely high complexity. The paper requires deep expertise in stochastic analysis, Poisson point processes, HJB PIDEs, viscosity solution theory, and forward-backward SDEs. The four progressively generalized models each require careful handling of non-local jump terms, state-dependent intensities, and diffusion components. Verification theorems involve intricate applications of Ito's formula for jump-diffusions, localization arguments, and transversality conditions. The FBSDE representation for the most general model requires familiarity with recursive utility theory and infinite-horizon BSDEs with jumps. No computational implementation is provided.

This is a purely theoretical mathematics paper with no numerical experiments, simulations, or code. All results are analytical proofs (verification theorems, viscosity solution existence). Reproducibility requires verifying the mathematical proofs independently. No computational implementation is provided. The paper builds on the framework of Brausmann and Bretschger (2024) [4] and uses standard tools from stochastic analysis.