This article develops a general framework for preference heterogeneity. This framework includes a discount function, a nonstandard Hamilton–Jacobi–Bellman equation (HJB) and a behavioral equation. When controlling parameters, our discount function and its HJB can reduce to those in Marín-Solano and Patxot (2012) and among many others. In various fields, our framework can find equilibrium path in the coexistence of present bias, preference heterogeneity, and time-inconsistency. As an example, the present paper quantifies the impact of preference heterogeneity on household financial decision-making. It has been proven that our nonstandard HJB yields sophisticated solution (i.e., equilibrium path ), while our behavioral equation brings about naive solution and precommitted solution.

中文翻译：

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偏好异质性及其均衡路径

本文开发了偏好异质性的一般框架。该框架包括一个贴现函数、一个非标准的 Hamilton-Jacobi-Bellman 方程 (HJB) 和一个行为方程。在控制参数时，我们的折扣函数及其 HJB 可以简化为 Marín-Solano 和 Patxot (2012) 等中的那些。在各个领域，我们的框架可以在当前偏差、偏好异质性和时间不一致的共存中找到平衡路径。例如，本文量化了偏好异质性对家庭财务决策的影响。已经证明，我们的非标准 HJB 产生了复杂的解决方案（即平衡路径），而我们的行为方程带来了朴素的解决方案和预提交的解决方案。