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

首席研究员将研究一些问题 在抽象的赌博理论中，这是一个特殊的公式， 随机控制，并在两个理论的相关问题， 个人零和随机博弈 一些研究将 处理有关最优奖励函数的基本问题， 赌博和随机博弈中的价值函数。 之一 对于一般的随机博弈类，这些问题是 价值的存在。 一些研究也将治疗 具体的随机控制问题和随机博弈。 最后还提出了一些问题的研究， 这是贝叶斯统计理论的一部分。 首席研究员将致力于基本的 关于最优决策的问题 不确定性的存在。 抽象赌博理论 一个决策者需要控制一个 以达到明确的目标。 在 两个参与者有相反的利益， 试图控制相同的过程，但朝向相反的目的。 的 这些问题的数学细节可能是高度技术性的， 但是解决方案在包括经济学在内的许多领域都是令人感兴趣的， 运筹学和金融。

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.