发表机构
Tsinghua University（清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对非指数折现的时间不一致正则-奇异控制问题，提出统一控制律的正则-奇异均衡和温和均衡概念，通过验证定理和HJB系统求解，在努力与分红问题中获得显式均衡并验证其性质。
AI 中文摘要
本文研究了连续时间下具有非指数折现的时间不一致混合正则-奇异控制问题。我们在人内博弈框架中寻求时间一致的均衡，并提出了一种新的正则-奇异均衡定义，其中正则控制和奇异控制通过控制律统一起来。我们建立了一个验证定理，为均衡提供了充分条件。此外，我们提出了温和均衡的新概念，其中扰动分别应用于正则控制和奇异控制，并给出了温和验证定理。我们通过求解扩展的Hamilton-Jacobi-Bellman（HJB）系统，在指数折现函数混合和伪指数折现函数下，将理论应用于努力与分红问题，并获得了依赖于努力阈值和分红阈值的显式均衡。值函数的凸性被严格建立，均衡条件得到验证。此外，我们在指数折现函数混合下建立了努力阈值和分红阈值的存在性。数值结果揭示了外生参数对努力阈值、分红阈值和均衡值函数的影响及其经济含义。
英文摘要
This paper studies a time-inconsistent mixed regular-singular control problem in continuous time with non-exponential discount. We seek time-consistent equilibria in an intrapersonal game framework and propose a novel definition of regular-singular equilibrium where both regular and singular controls are unified via control laws. We establish a verification theorem to provide a sufficient condition of the equilibrium. Furthermore, we propose a novel concept of mild equilibrium for which perturbations are applied separately to the regular and singular control and give the mild verification theorem. We illustrate the applicability of the theory to the effort and dividend problem and obtain an explicit equilibrium depending on the effort and dividend thresholds under a mixture of exponential discount functions and a pseudo-exponential discount function by solving the extended Hamilton--Jacobi--Bellman (HJB) system. The convexity of the value function is rigorously established, and the equilibrium conditions are verified. In addition, we establish the existence of the effort and dividend thresholds under a mixture of exponential discount functions. Numerical results reveal the impacts of exogenous parameters on the effort and dividend thresholds and the equilibrium value function, along with their economic implications.
