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On a Robust Approach for Stochastic Equilibrium Problems

随机平衡问题的鲁棒方法

基本信息

批准号：
EP/J014427/1
负责人：
Huifu Xu
金额：
$ 2.62万
依托单位：
University of Southampton
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2012
资助国家：
英国
起止时间：
2012 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FJ014427%2F1
关键词：
Robust Approach Stochastic Equilibrium Problems

项目摘要

Stochastic programming has been extensively used by operation researchers, economists and various decision makers/practitioners to model optimal decision making in economics, management, engineering, transportation networks and the environment. When a decision problem involves not only uncertainty, but also severaldecision makers who are in a competitive relationship, it becomes a stochastic game. An important approach in understanding such a game is to look at the equilibrium outcomes. These are the set of possible outcomes atthe end of competition, given that each player seeks to optimize their own payoff.A fundamental issue in stochastic programming and equilibrium concerns the representation ofuncertainty. Many of the models in the literature assume complete knowledge of the distributions of random variables (representing the uncertainty). Inmany practical cases, however, such distributions are not known precisely and have to be either estimated from historical data or constructed usingsubjective judgements. The available information is often insufficient to give confidence in the distribution identified. In the absence of full information on the underlying distribution, it may still be possible toidentify a set of possible probability distributions within which the true distribution lies. While a robust optimization approach to this problem isbased on making the decision that would be appropriate given the worst probability distribution in the set of possible distributions, robust analysis of stochastic equilibrium is to look into worst equilibrium outcomes given the incomplete information of the underlying stochastic elements and robust designrequires one to set out optimal policy/parameters which accommodate any worst equilibrium outcomes.The project is proposed to develop a mathematical framework that allows one to carry out robust anaysis of a stochastic equilibrium problem with incomplete information on the underlying uncertainty, identify optimal policy/design which accommodate the worst possible equilibrium outcomes, develop efficient numerical methods for solving the new mathematical models and apply apply them to some interesting practical problems in economics and engineering with a particular focus on energy industry.

随机规划已被广泛使用的操作研究人员，经济学家和各种决策者/从业者在经济，管理，工程，交通网络和环境的最佳决策模型。当一个决策问题不仅涉及不确定性，而且涉及多个处于竞争关系的决策者时，它就成为一个随机博弈。理解这样一个博弈的一个重要方法是看均衡结果。这些是在竞争结束时的一组可能的结果，假设每个参与者都寻求优化自己的收益。随机规划和均衡中的一个基本问题涉及不确定性的表示。文献中的许多模型假设完全了解随机变量的分布（表示不确定性）。然而，在许多实际情况下，这种分布并不精确，必须从历史数据中估计或使用主观判断构建。现有资料往往不足以使人相信所确定的分布情况。在缺乏关于潜在分布的完整信息的情况下，仍然有可能确定一组可能的概率分布，真实分布位于其中。虽然对这个问题的鲁棒优化方法是基于在给定可能分布集中的最差概率分布的情况下做出适当的决策，随机均衡的鲁棒分析是考虑潜在随机元素的不完全信息的最坏均衡结果，鲁棒设计要求制定最优策略。该项目提出了一个数学框架，允许一个进行强大的分析的随机平衡问题与不完全信息的基本不确定性，确定最佳的政策/设计，以适应最坏的可能的均衡结果，开发有效的数值方法来解决新的数学模型，并将其应用于经济和工程中的一些有趣的实际问题，特别是能源行业。