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arXiv · 2511.08433

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

Jingyi Cao·Dongchen Li·Virginia R. Young·Bin Zou
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Abstract

We revisit the optimal dividend problem of de Finetti by adding a variance term to the usual criterion of maximizing the expected discounted dividends paid until ruin, in a singular control framework. Investors do not like variability in their dividend distribution, and the mean-variance (MV) criterion balances the desire for large expected dividend payments with small variability in those payments. The resulting MV singular dividend control problem is time-inconsistent, and we follow a game-theoretic approach to find a time-consistent equilibrium strategy. Our main contribution is a new verification theorem for the novel dividend problem, in which the MV criterion is applied to an integral of the control until ruin, a random time that is endogenous to the problem. We demonstrate the use of the verification theorem in two cases for which we obtain the equilibrium dividend strategy (semi-)explicitly, and we provide a numerical example to illustrate our results.

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Jingyi Cao, Dongchen Li, Virginia R. Young, Bin Zou. 2025-11-11. Equilibrium Strategies for Singular Dividend Control Problems under the Mean-Variance Criterion. https://arxiv.org/abs/2511.08433

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