Mathematical Sciences: Abstract Gambling Theory, Stochastic Games, and Statistics

数学科学：抽象赌博理论、随机博弈和统计学

• 批准号: 9123358
• 负责人: William Sudderth
• 金额: $ 7.5万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9123358&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Abstract; Gambling; Theory

The principal investigator will work on a number of problems in abstract gambling theory, which is a particular formulation of stochastic control, and on related problems in the theory of two- person, zero-sum stochastic games. Some of the research will treat fundamental questions about the optimal reward function in gambling and the value function in stochastic games. One of these questions for a general class of stochastic games is the existence of the value. Some of the research will also treat specific stochastic control problems and stochastic games. Finally research is also proposed on certain questions which arise in the theory of Bayesian statistics. The principal investigator will work on fundamental questions about optimal decision making through time in the presence of uncertainty. Abstract gambling theory treats problems in which a single decision maker needs to control a process so as to attain some well-defined objective. In stochastic games two players have opposing interests and each seeks to control the same process but toward opposite ends. The mathematical details of such problems can be highly technical, but solutions are of interest in many areas including economics, operations research, and finance.

首席研究员将研究抽象赌博理论中的一些问题，这是随机控制的一个特殊公式，以及二人零和随机博弈理论中的相关问题。一些研究将处理赌博中的最优奖励函数和随机博弈中的价值函数等基本问题。对于一般类型的随机对策，其中一个问题是值的存在性。一些研究还将处理特定的随机控制问题和随机博弈。最后对贝叶斯统计理论中出现的几个问题进行了研究。首席研究员将研究在存在不确定性的情况下通过时间进行最佳决策的基本问题。抽象赌博理论处理的问题是，单个决策者需要控制一个过程，以达到某些明确的目标。在随机博弈中，两个玩家有着相反的利益，每个人都试图控制相同的过程，但走向相反的目标。这些问题的数学细节可能是高度技术性的，但解决方案在许多领域都很有趣，包括经济学、运筹学和金融学。