Dividend ratcheting and capital injection under the Cramér-Lundberg model: Strong solution and optimal strategy

Battle Count: 109

This paper is primarily relevant to actuarial science and insurance risk management rather than quantitative trading. The Cramér-Lundberg model and dividend ratcheting problem are specific to insurance company surplus management. However, the mathematical techniques (HJB variational inequalities with gradient constraints, free boundary problems, regime-switching approximations for integro-differential equations) have indirect relevance to optimal execution, portfolio management with constraints, and stochastic control problems in quantitative finance. The jump-diffusion framework and capital injection concepts have some parallels to trading with transaction costs and margin requirements.

Extremely high complexity. The paper requires deep expertise in: (1) stochastic optimal control theory, (2) partial integro-differential variational inequalities, (3) free boundary problems, (4) regime-switching systems, (5) comparison principles for nonlocal operators, (6) Arzela-Ascoli compactness arguments, and (7) Itô calculus for jump processes. The proofs span approximately 30 pages of dense mathematical analysis. No computational implementation is provided. The theoretical framework is highly specialized and would require significant adaptation for practical use.

This is a pure mathematics paper with self-contained proofs. All definitions, lemmas, theorems, and proofs are provided in the paper (including Appendix A). The methodology is fully described and does not require external data or code. However, the proofs are highly technical and require deep expertise in PDE theory, stochastic control, and integro-differential equations to verify independently. No computational experiments are needed.