ROBUST CONTROL FOR MARKED POINT PROCESSES UNDER TRANSITION-RATE UNCERTAINTY

Battle Count: 75

The paper is primarily focused on actuarial science and insurance mathematics rather than quantitative trading. However, the robust control framework, max-min optimization, and BSDE methodology have conceptual parallels with robust portfolio optimization and risk management in financial markets. The marked point process framework could theoretically be adapted to model jump processes in financial contexts, but the paper does not explore this direction. The power utility consumption-insurance problem has structural similarities to Merton-type portfolio problems but is applied to biometric rather than financial risk.

The mathematical framework is highly complex, involving: (1) canonical filtered measurable spaces for marked point processes, (2) jump-count and state-wise decompositions of optional/predictable processes, (3) non-standard BSDEs with accessible jump times and non-Lipschitz generators, (4) infinite systems of Lebesgue-Stieltjes integral equations, (5) Banach fixed-point arguments in BV spaces with equivalent norms, and (6) verification theorems requiring careful integrability conditions. Practical implementation would require significant expertise in stochastic analysis, measure theory, and actuarial mathematics. No computational algorithms or code are provided.

The paper is entirely theoretical with complete mathematical proofs. All results are self-contained with explicit definitions, assumptions, and step-by-step proofs. The canonical marked point process framework is well-defined. However, no numerical examples or code are provided for practical implementation. The semi-Markov example (Example 5.3) provides a concrete instantiation but no numerical solutions are computed.