不确定性和风险性管理决策的理论和应用研究

Modern decision makers have to make decisions under highly uncertain environment in spite of experiencing a giant risk . A successful decision gave encouragement and satisfactory to the managers, however, the gloomy shadow of decision failures is always wandering among the decision makers. Since the mid of last century, scientists continuously explore the theory and methodology for making decisions scientifically under the environment of uncertainty , the purpose for which is to obtain a maximum utility of decisions while experienced minimum risks subject to lowest amount of losses. Since the expected utility theory under uncertainty suggested by Von Neumann & Morganstein , Wald proposed a statistical decision theory, Bayes decision theory was raised by Raiffe & Schlaifer ,the famous mean and variance theory of Markowitz was created in 1950's, in recent years, Jia & Dyer put forward their risk/return theory in 90's etc,scientists and researchers have got significant theoretical results in recent years. Motivated by these sound acheivements, we suggested our proposal for this research project and fortunately got the approval and financial support from the NSFC in 2000.We have been researching into the theory of decision making under uncertainty based on entropy, in addition, we also researching into the theory and methodology for sequential decision making in simulation environment for the purpose of creating a bridge between theory and application. The following research subjects in the above two directions were underway during the period of this project: The research of risk measurement based on expected utility and entropy model, The Bayes decision theory based on entropy, The uncertain portfolio investment decision model with no probability assumptions of environment, The sequential decision theory and models under the environment of virtual reality simulation, Simulation/optimization theory and algorithms for dynamic and stochastic sequential decision making, and The evidence theory for solving the occurrence probability of uncertain important and rare events. These researches have got some original idea and results in those areas.. The main research results are as follows : The uncertain status are transferred to the probability distributions based on the utility-entropy risk measurement model ,so as to transfer an uncertain decision problem into a risky decision model. The mathematical description of EMV* and EVSI are obtained based on the entropy posterior decision theory. Besides, the general entropy decision model is extended to group decision area in accordance with the concept of relative entropy. The decision problems under uncertainty can be solved by 3W+N mechanism based on the theory of sequential decision making in a virtual reality simulation environment, especially The theory and algorithm of transient decision path allowing the decision makers to make real-time decisions for obtaining predefined optimum objectives. The dynamic optimization theory and algorithms for selecting optimal decision series under uncertainty are also suggested. The evidence-merging algorithm can give an estimation of probability of rare events occurance in an uncertain decision problem and the consequences of the event can be analysed via simulation , in addition, the optimal decision for responding the rare events is also given. .

在现代社会中，人们往往需要在高度不确定性的经济、技术环境中，甘冒巨大的风险作出必要的决策。成功的决策将极大地鼓舞和激励管理者，然而，决策失误的阴影也时刻在决策者之间游荡。半个世纪以来，人们不断地探索在不确定性条件下进行科学决策的理论和方法，以期以最低的风险和损失，获得最大的决策效用和成果。从Von Neumann & Morganstein的不确定条件下的期望效用理论、Wald 的统计决策理论、Raiffe & Schlaifer 的Bayes决策理论到Markowitz的均值方差理论，以及90年代以来Jia & Dyer的风险价值理论，取得了显著的理论研究成果。在此背景下我们提出本课题的申请，并得到国家自然基金的资助。. 本课题研究除了对不确定条件下基于熵的决策理论进行研究外，也对仿真环境下的序贯决策理论和方法进行了研究，以期建立决策理论与应用间的桥梁。在这两个方向上进行以下理论与方法的研究：对基于期望效用-熵的风险度量理论模型，基于熵的Bayes决策理论，无概率假设的不确定性组合投资决策模型，虚拟现实仿真环境下的序贯决策理论和模型，动态随机序贯决策的仿真优化理论和算法，不确定性重要稀有事件发生概率的证据推理理论等内容进行了研究，具有一定的创新性。. 所研究内容的主要结果：基于期望效用-熵的风险度量模型将不确定状态转化为状态的概率分布，从而将不确定性决策问题转化为风险性决策问题。基于熵的Bayes后验决策理论，得到EMV*和EVSI的数学描述，并根据相对熵概念将一般熵决策模型推广到群决策领域。基于虚拟现实仿真的序贯决策理论使不确定性决策问题在3W+N模式下得到解决，特别是瞬态决策路径理论和算法可在不确定环境中进行实时决策，达到预定优化目标。提出了不确定性决策中决策序列的动态最优化理论和算法，为决策者提供最优决策序列。基于证据推理融合算法，可对不确定性决策问题