Optimal Dividend, Reinsurance, and Capital Injection for Collaborating Business Lines under Model Uncertainty

Battle Count: 88

The paper is primarily focused on insurance risk management and actuarial science rather than quantitative trading. However, the robust control framework, barrier strategies, and model uncertainty treatment have conceptual parallels with portfolio optimization under model misspecification. The diffusion process modeling and HJB equation techniques are transferable to financial applications. The relative entropy penalty approach is relevant to robust portfolio selection. The paper's relevance to trading is indirect, primarily through shared mathematical methodology.

The analytical solutions are fully derived in closed form, making implementation straightforward once the parameter regime is identified. However, determining which of the three scenarios applies requires solving the polynomial equation psi(z)=0 and checking multiple technical conditions involving the relative Sharpe ratio, correlation, and ambiguity-aversion parameters. The barrier strategy implementation requires tracking aggregate reserves and managing capital transfers between lines. The numerical computation of optimal reinsurance and distortion levels involves evaluating complex expressions with multiple parameters.

The paper provides complete closed-form analytical solutions (value functions and optimal strategies) across all parameter regimes. All base parameter values for numerical illustrations are explicitly stated in Table 1. The mathematical derivations are fully presented in the main text and appendices. However, no code or supplementary computational files are mentioned. The analytical nature of the results makes them highly reproducible given the stated parameters.