Equilibrium Strategies for Singular Dividend Control Problems under the Mean-Variance Criterion

Battle Count: 107

While the paper is primarily about insurance/actuarial dividend optimization rather than trading, the mean-variance framework, time-inconsistency handling via game theory, and singular control techniques have indirect relevance to quantitative trading. The MV criterion and equilibrium concepts could inform risk-aware portfolio strategies. However, the specific application (dividend distribution until ruin) is more relevant to corporate finance and insurance than to trading.

The theoretical framework involves solving extended HJB systems with three coupled functions (V, G, H), variational inequalities, and Skorokhod reflection problems. The verification theorem proof is technically demanding. Numerical implementation requires solving nonlinear equations for the barrier and computing exponential functions with multiple parameters. The mathematical sophistication is high, though the final formulas are semi-explicit.

The paper provides complete mathematical proofs, explicit formulas for equilibrium strategies, and numerical examples with specific parameter values (a=1, b=0.25, ρ=0.2). However, no code repository is provided. The numerical analysis is described but implementation details are limited. The theoretical results are fully self-contained with detailed proofs.