Stochastic Games for Intergenerational Equity in Mathematical Finance

数学金融中代际公平的随机博弈

• 批准号: 1715439
• 负责人: Yu-Jui Huang
• 金额: $ 18.62万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-01 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1715439&HistoricalAwards=false
• 关键词: Stochastic; Games; Intergenerational; Equity; Mathematical

Intergenerational conflicts of interest are inevitable to wealth and resource management in a society. This problem is more pressing now than ever as demographic change has reached a pivotal point. The combined working-age population in developed countries is projected to shrink continuously until 2050, while the retired population will grow rapidly. The tension between the two cohorts, working and retired (or, young and old), is almost certain to exacerbate, as the wealth of the former is used to support the latter, under Social Security or many other pension schemes. Yet, the precise economic consequences are not that apparent. This project aims to elucidate how an evolving demographic structure affects financial planning in a society. This will be done at two different levels: one from the eyes of the competing young and old cohorts, the other from the panoramic perspective of a social planner, such as a government. Graduate students are involved in the project. The first part of the project investigates the interplay between the young and the old cohorts. It is formulated as a two-player nonzero-sum game in a stochastic Ramsey model, with the dynamics of demographic structure explicitly modeled. The goal is to understand how the two cohorts interact through their consumption and saving decisions, and how an evolving demographic structure affects their decisions, and the resulting welfare. Nash equilibrium strategies of the two cohorts will be found and analyzed through a system of coupled Hamilton-Jacobi-Bellman equations with non-Lipschitz coefficients. This demands new developments in stochastic differential games and viscosity solution techniques. The second part of the project handles the social planner's dilemma: a financial planning strategy deemed optimal today by the current society may not be optimal from the view of the society in the future, as the evolving demographics continuously change the overall societal preference. This leads to a new form of time-inconsistent problems, with non-exponential and time-dependent discount functions, which will be treated under an intra-personal game between current and future societies. A new method for time-inconsistency, called the fixed-point approach, is developed in the project. It provides a new machinery for constructing time-consistent strategies, while possessing the potential of less mathematical technicalities.

代际利益冲突是社会财富和资源管理中不可避免的问题。这个问题现在比以往任何时候都更加紧迫，因为人口变化已经到了一个关键点。预计发达国家的劳动年龄人口总和将持续减少，直到2050年，而退休人口将迅速增长。工作和退休（或年轻人和老年人）这两个群体之间的紧张关系几乎肯定会加剧，因为前者的财富在社会保障或许多其他养老金计划下被用来支持后者。然而，确切的经济后果并不那么明显。本项目旨在阐明不断变化的人口结构如何影响社会的财务规划。这将在两个不同的层面上完成：一个是从竞争的年轻人和老年人的角度，另一个是从社会规划者的全景视角，如政府。研究生参与了这个项目。该项目的第一部分调查了年轻人和老年人之间的相互作用。它被制定为一个两个球员的非零和游戏中的随机拉姆齐模型，明确建模的人口结构的动态。我们的目标是了解这两个群体如何通过他们的消费和储蓄决策相互作用，以及不断变化的人口结构如何影响他们的决策以及由此产生的福利。纳什均衡策略的两个队列将被发现和分析通过一个系统的耦合的非Lipschitz系数的Hamilton-Jacobi-Bellman方程。这就要求在随机微分对策和粘性解技术方面有新的发展。该项目的第二部分处理了社会规划师的困境：当前社会认为最优的财务规划策略可能不是未来社会的最优策略，因为不断变化的人口统计不断改变整体社会偏好。这导致了一种新形式的时间不一致的问题，非指数和时间依赖的折扣函数，这将被视为当前和未来社会之间的个人内部游戏。在该项目中，开发了一种新的时间不一致性方法，称为固定点方法。它提供了一种新的机制，用于构建时间一致的策略，同时拥有较少的数学技术细节的潜力。

项目成果

Optimal Consumption in the Stochastic Ramsey Problem without Boundedness Constraints

• DOI: 10.1137/18m1188410
• 发表时间: 2018-05
• 期刊: SIAM J. Control. Optim.
• 作者: Yu‐Jui Huang;S. Khalili

Optimal equilibria for time‐inconsistent stopping problems in continuous time

时间的最优平衡——连续时间内的不一致停止问题

• DOI: 10.1111/mafi.12229
• 发表时间: 2019
• 期刊: Mathematical Finance
• 影响因子: 1.6
• 作者: Huang, Yu‐Jui;Zhou, Zhou
• 通讯作者: Zhou, Zhou

Optimal Equilibria for Multidimensional Time-Inconsistent Stopping Problems

多维时间不一致停止问题的最优平衡

• DOI: 10.1137/20m1343774
• 发表时间: 2021
• 期刊: SIAM Journal on Control and Optimization
• 影响因子: 2.2
• 作者: Huang, Yu-Jui;Wang, Zhenhua
• 通讯作者: Wang, Zhenhua

Strong and Weak Equilibria for Time-Inconsistent Stochastic Control in Continuous Time

连续时间内时间不一致随机控制的强弱均衡

• DOI: 10.1287/moor.2020.1066
• 发表时间: 2021
• 期刊: Mathematics of Operations Research
• 影响因子: 1.7
• 作者: Huang, Yu-Jui;Zhou, Zhou
• 通讯作者: Zhou, Zhou

The Optimal Equilibrium for Time-Inconsistent Stopping Problems---The Discrete-Time Case

时间不一致停止问题的最优平衡--离散时间情况

• DOI: 10.1137/17m1139187
• 发表时间: 2019
• 期刊: SIAM Journal on Control and Optimization
• 影响因子: 2.2
• 作者: Huang, Yu-Jui;Zhou, Zhou
• 通讯作者: Zhou, Zhou