Equilibrium singular dividend control under ambiguity aggregation of heterogeneous discount rates

Battle Count: 159

The paper is primarily relevant to corporate finance and actuarial science rather than quantitative trading. It addresses dividend policy optimization for firms with heterogeneous shareholders, which is tangentially related to dividend-paying stock strategies. The mathematical techniques (stochastic control, verification theorems, Skorokhod reflection) are relevant to the broader quantitative finance toolkit, but the specific problem of dividend control under ambiguity aggregation has limited direct application to trading strategies, market making, or algorithmic execution.

The paper involves highly advanced mathematical machinery including: generalized Ito formula for semimartingales, Skorokhod reflection problems, variational inequalities with aggregate weighted marginal conditions, Chebyshev integral inequality for non-existence proofs, and detailed perturbation analysis for equilibrium verification. Implementing the numerical solution of the equilibrium barrier requires solving ODEs with boundary conditions and root-finding for the aggregate smooth-pasting condition. The theoretical framework requires deep expertise in stochastic analysis, optimal control, and mathematical finance.

The paper is primarily theoretical with rigorous mathematical proofs. Numerical examples (Section 6) provide specific parameter values (mu=0.1, sigma=0.2, r1=0.03, r2=0.07) and equilibrium conditions that can be reproduced. However, no code or computational scripts are provided. The theoretical results require advanced knowledge of stochastic analysis, Skorokhod reflection problems, and variational inequalities to verify independently.