Risk Assessment and Decision Making Under Uncertainty with Applications

本课题研究随机模型在社会科学中的应用及其数学基础。第一部分涉及气候变化的经济学。气候变化可能是一个影响非常大的全球风险；缓解气候变化是一项涉及众多科学和机构的跨学科挑战。第二部分研究随机博弈中个体偏好如何导致集体行为；这有助于理解具有许多决策者的系统中的宏观效应，例如证券市场中的金融危机。第三部分考察了市场参与者异质性导致的资产市场投机性价格泡沫的产生。第四部分研究了某些随机过程的概率密度的存在性，并给出了这些密度的估计。气候响应及其与经济相互作用的复杂性导致了模型的模糊性和决策中的随机不确定性。然而，现有文献在很大程度上依赖于确定性模型。该项目旨在强调不确定性和模糊性对风险评估和政策制定的影响，以及启动从数学金融等经常使用随机模型的领域转移知识。关于随机博弈，该项目研究具有平均场相互作用的模型，至少在形式上，对应于具有连续玩家的博弈。均衡的多重性与主体的联盟有关，稳定性的概念可能有助于理解为什么平均场博弈的某些均衡是n人博弈的极限，而其他均衡则不是。第三个项目将继续最近的工作，旨在为异质代理人之间的投机开发一个强大的随机模型，并研究市场监管和市场参与者之间的信念分布如何影响泡沫中的价格和投机交易。随机过程的概率密度研究采用了一种基于最优控制理论的新方法。它允许非常普遍的过程，包括非马尔可夫过程，而本质上是基本的。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project studies stochastic models applied in social sciences as well as their mathematical foundations. The first part concerns the economics of climate change. Climate change could be a very impactful global risk; its mitigation becomes an interdisciplinary challenge involving a multitude of sciences and agencies. The second part studies how collective behavior can result from individual preferences in stochastic games; this is useful to understand macroscopic effects in systems with many decision-takers, such as financial crises in securities markets. The third part investigates the emergence of speculative price bubbles in asset markets as a consequence of heterogeneity among market participants. The fourth part studies the existence of probability densities for certain stochastic processes and produces estimates for these densities.The complexity of the climate response and its interaction with the economy gives rise to model ambiguity and stochastic uncertainty in decision making. Nevertheless, the existing literature largely relies on deterministic models. This project aims to emphasize the impact of uncertainty and ambiguity on risk assessment and policy making, as well as initiating a transfer of knowledge from fields such as mathematical finance where stochastic models are routinely employed. Regarding stochastic games, the project studies models with mean field interaction which, at least formally, correspond to games with a continuum of players. It is expected that multiplicity of equilibria is related to coalitions of agents, and a notion of stability may be useful to understand why certain equilibria of mean field games are limits of N-player games but others are not. The third project will continue recent work that aims to develop a robust stochastic model for speculation among heterogeneous agents and investigate how market regulations and the distribution of beliefs among market participants influence prices and speculative trading in a bubble. The study of probability densities for stochastic processes follows a novel approach based on optimal control theory. It allows for remarkably general processes, including non-Markovian ones, while being elementary in nature.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.