Refined Approximation of Tail Probabilities, Constrained Expectations, Data Analysis in Multidimensional and Metric Spaces, Plus Optimal Stable Growth in Finance

尾部概率的精细逼近、约束期望、多维和度量空间的数据分析以及金融领域的最优稳定增长

• 批准号: 0205054
• 负责人: Michael Klass
• 金额: --
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-15 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0205054&HistoricalAwards=false
• 关键词: Refined; Approximation; Tail; Probabilities; Constrained

0205054Klass In work with various co-authors, the PI plans to work on the following five tasks. 1) Complete a paper on (nearly optimal) approximation of quantile location for sums of independent and otherwise arbitrary random variables. 2) Complete a paper in finance which introduces a new constraint to augment the optimal growth criterion and thereby provide local wealth stability. A natural sub-optimal strategy can be exhibited. It is further shown how one can create a long-term portfolio strategy which asymptotically withdraws money at the (same) asymptotic rate at which the portfolio is growing, without diminishing that long-term rate(!). 3) Extend previous work on self-normalized martingales. 4) Attempt to construct and/or identify extremal distributions which arise in various situations maximizing the expected value of some random quantity subject to infinitely many linear inequality constraints. 5) Develop an idea, conveyed to him in 1992 by Prof. David L. Allen, to show how to construct a natural posterior distribution on densities in R, given only the data acquired, and extending the result to R^d by means of the Radon Transform. This approach permits one to establish confidence intervals for parameter estimation, to perform hypothesis testing and data classification with only finite samples. Goodness of fit tests are also contemplated. The principle investigator plans work in five areas: quantile approximation for sums of arbitrary independent random variables, optimal investment strategy designed to guard against local capital losses of more than a pre-set proportion of the previous maximal accumulated wealth (plus a method of permitting consumption at the long run growth rate without sacrificing that long-run rate), extend previous work on self-normalized martingales, solve or find approximately optimal solutions to certain infinite dimensional linear programming problems, demonstrate how to make full use of the data acquired in statistical settings which involve hypothesis testing or classification (categorization) of data. The investment work should be of fundamental interest and importance to individual, corporate and community (governmental) investment. The data analysis efforts may suggest a best possible approach to determining whether a particular datum came from A or B given limited prior data on A and B. Such work could be useful in character recognition, hand-writing decipherment, etc. The other topics were motivated by prior work of the PI.

0205054 Klass在与各种合著者的合作中，PI计划开展以下五项任务。1)完成一篇关于独立和任意随机变量之和的分位数位置的（近最优）近似的论文。2)完成一篇金融学论文，其中引入了一个新的约束来增强最优增长标准，从而提供了局部财富稳定性。可以展示自然的次优策略。它进一步表明，如何可以创建一个长期的投资组合策略，渐近撤回资金在（相同）的渐近速度，投资组合的增长，而不会减少长期利率（！）。3)推广了以前关于自正规鞅的工作。4)尝试构造和/或识别极值分布，这些分布出现在各种情况下，最大化受无穷多个线性不等式约束的某个随机量的期望值。5)发展一个想法，由大卫教授在1992年告诉他。艾伦，以显示如何构建一个自然的后验分布的密度在R中，只给定所获得的数据，并扩展结果的R^d通过拉东变换。这种方法允许建立参数估计的置信区间，进行假设检验和数据分类，只有有限的样本。还考虑拟合优度测试。 首席调查员计划在五个领域开展工作：任意独立随机变量之和的分位数近似，最优投资策略旨在防止局部资本损失超过先前最大累积财富的预设比例（加上一种允许消费在长期增长率而不牺牲长期增长率的方法），扩展了以前关于自归一化鞅的工作，解决或找到近似最佳的解决方案，以某些无限维线性规划问题，演示如何充分利用在统计设置，其中涉及假设检验或数据分类（归类）所获得的数据。投资工作应该是个人、公司和社区（政府）投资的根本利益和重要性。数据分析工作可能会提出一种最佳可能方法，以确定特定数据是否来自A或B，因为A和B的先验数据有限。这项工作可能是有用的字符识别，手写破译等其他主题的动机由PI以前的工作。