{"ID":2848950,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.24128","arxiv_id":"2510.24128","title":"Extended HJB Equation for Mean-Variance Stopping Problem: Vanishing Regularization Method","abstract":"This paper studies the time-inconsistent MV optimal stopping problem via a game-theoretic approach to find equilibrium strategies. To overcome the mathematical intractability of direct equilibrium analysis, we propose a vanishing regularization method: first, we introduce an entropy-based regularization term to the MV objective, modeling mixed-strategy stopping times using the intensity of a Cox process. For this regularized problem, we derive a coupled extended Hamilton-Jacobi-Bellman (HJB) equation system, prove a verification theorem linking its solutions to equilibrium intensities, and establish the existence of classical solutions for small time horizons via a contraction mapping argument. By letting the regularization term tend to zero, we formally recover a system of parabolic variational inequalities that characterizes equilibrium stopping times for the original MV problem. This system includes an additional key quadratic term--a distinction from classical optimal stopping, where stopping conditions depend only on comparing the value function to the instantaneous reward.","short_abstract":"This paper studies the time-inconsistent MV optimal stopping problem via a game-theoretic approach to find equilibrium strategies. To overcome the mathematical intractability of direct equilibrium analysis, we propose a vanishing regularization method: first, we introduce an entropy-based regularization term to the MV...","url_abs":"https://arxiv.org/abs/2510.24128","url_pdf":"https://arxiv.org/pdf/2510.24128v1","authors":"[\"Yuchao Dong\",\"Harry Zheng\"]","published":"2025-10-28T07:06:29Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"q-fin.MF\"]","methods":"[\"Large Language Model\"]","has_code":false}